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Exercícios de exponenciais e logaritmos · Physics Playground

ExercíciosMatemática

Exponenciais e logaritmos

75 problemas com soluções resolvidas, de Algebra and Trigonometry.

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Aprenda antes: Crescimento e Decaimento Exponencial, Logaritmos

Algebra and Trigonometry6.1 Exponential Functions

Exemplo 1Identifying Exponential FunctionsWhich of the following equations are not exponential functions? f(x)=4^(3( x−2)) g(x)=x^3 h(x)= ( 1/3) ^x j(x)= ( −2) ^xMais um parecido para tentar
Exemplo 2Evaluating Exponential FunctionsLet f( x)=5 ( 3) ^(x+1). Evaluate f( 2) without using a calculator.Mais um parecido para tentar
Exemplo 3Evaluating a Real-World Exponential ModelAt the beginning of this section, we learned that the population of India was about 1.25 billion in the year 2013, with an annual growth rate of about 1.2%. This situation is represented by the growth function…Mais um parecido para tentar
Exemplo 4Writing an Exponential Model When the Initial Value Is KnownIn 2006, 80 deer were introduced into a wildlife refuge. By 2012, the population had grown to 180 deer. The population was growing exponentially. Write an exponential function N(t) representing the population ( N) of…Mais um parecido para tentar
Exemplo 5Writing an Exponential Model When the Initial Value is Not KnownFind an exponential function that passes through the points ( −2,6) and ( 2,1).Mais um parecido para tentar
Exemplo 6Writing an Exponential Function Given Its GraphFind an equation for the exponential function graphed in Figure 5. Figure 5Com figuraMais um parecido para tentar
Exemplo 7Using a Graphing Calculator to Find an Exponential FunctionUse a graphing calculator to find the exponential equation that includes the points (2,24.8) and (5,198.4).Mais um parecido para tentar
Exemplo 8Calculating Compound InterestIf we invest $3,000 in an investment account paying 3% interest compounded quarterly, how much will the account be worth in 10 years?Mais um parecido para tentar
Exemplo 9Using the Compound Interest Formula to Solve for the PrincipalA 529 Plan is a college-savings plan that allows relatives to invest money to pay for a child’s future college tuition; the account grows tax-free. Lily wants to set up a 529 account for her new granddaughter and…Mais um parecido para tentar
Exemplo 10Using a Calculator to Find Powers of eCalculate e^(3.14). Round to five decimal places.Mais um parecido para tentar
Exemplo 11Calculating Continuous GrowthA person invested $1,000 in an account earning a nominal 10% per year compounded continuously. How much was in the account at the end of one year?Mais um parecido para tentar
Exemplo 12Calculating Continuous DecayRadon-222 decays at a continuous rate of 17.3% per day. How much will 100 mg of Radon-222 decay to in 3 days?Mais um parecido para tentar

Algebra and Trigonometry6.2 Graphs of Exponential Functions

Exemplo 1Sketching the Graph of an Exponential Function of the Form f(x) = bxSketch a graph of f(x)= 0.25 ^x. State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 2Graphing a Shift of an Exponential FunctionGraph f(x)=2^(x+1) −3. State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 3Approximating the Solution of an Exponential EquationSolve 42=1.2 ( 5) ^x +2.8 graphically. Round to the nearest thousandth.Mais um parecido para tentar
Exemplo 4Graphing the Stretch of an Exponential FunctionSketch a graph of f(x)=4 ( 1/2) ^x. State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 5Writing and Graphing the Reflection of an Exponential FunctionFind and graph the equation for a function, g(x), that reflects f(x)= ( 1/4) ^x about the x-axis. State its domain, range, and asymptote.Mais um parecido para tentar
Exemplo 6Writing a Function from a DescriptionWrite the equation for the function described below. Give the horizontal asymptote, the domain, and the range. f(x)=e^x is vertically stretched by a factor of 2, reflected across the y-axis, and then shifted up 4 units.Mais um parecido para tentar

Algebra and Trigonometry6.3 Logarithmic Functions

Exemplo 1Converting from Logarithmic Form to Exponential FormWrite the following logarithmic equations in exponential form. ⓐ log6 ( √6)=1/2 ⓑ log3 ( 9)=2Mais um parecido para tentar
Exemplo 2Converting from Exponential Form to Logarithmic FormWrite the following exponential equations in logarithmic form. 2^3 =8 5^2 =25 10 ^(−4) =1/(10,000)Mais um parecido para tentar
Exemplo 3Solving Logarithms MentallySolve y=log4 ( 64) without using a calculator.Mais um parecido para tentar
Exemplo 4Evaluating the Logarithm of a ReciprocalEvaluate y=log3 ( 1/(27)) without using a calculator.Mais um parecido para tentar
Exemplo 5Finding the Value of a Common Logarithm MentallyEvaluate y=log(1000) without using a calculator.Mais um parecido para tentar
Exemplo 6Finding the Value of a Common Logarithm Using a CalculatorEvaluate y=log( 321) to four decimal places using a calculator.Mais um parecido para tentar
Exemplo 7Rewriting and Solving a Real-World Exponential ModelThe amount of energy released from one earthquake was 500 times greater than the amount of energy released from another. The equation 10 ^x =500 represents this situation, where x is the difference in magnitudes on…Mais um parecido para tentar
Exemplo 8Evaluating a Natural Logarithm Using a CalculatorEvaluate y=ln( 500) to four decimal places using a calculator.Mais um parecido para tentar

Algebra and Trigonometry6.4 Graphs of Logarithmic Functions

Exemplo 1Identifying the Domain of a Logarithmic ShiftWhat is the domain of f(x)=log2 (x+3)?Mais um parecido para tentar
Exemplo 2Identifying the Domain of a Logarithmic Shift and ReflectionWhat is the domain of f(x)=log(5−2x)?Mais um parecido para tentar
Exemplo 3Graphing a Logarithmic Function with the Form f(x) = logb(x).Graph f(x)=log5 ( x). State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 4Graphing a Horizontal Shift of the Parent Function y = logb(x)Sketch the horizontal shift f(x)=log3 (x−2) alongside its parent function. Include the key points and asymptotes on the graph. State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 5Graphing a Vertical Shift of the Parent Function y = logb(x)Sketch a graph of f(x)=log3 (x)−2 alongside its parent function. Include the key points and asymptote on the graph. State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 6Graphing a Stretch or Compression of the Parent Function y = logb(x)Sketch a graph of f(x)=2log4 (x) alongside its parent function. Include the key points and asymptote on the graph. State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 7Combining a Shift and a StretchSketch a graph of f(x)=5log(x+2). State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 8Graphing a Reflection of a Logarithmic FunctionSketch a graph of f(x)=log(−x) alongside its parent function. Include the key points and asymptote on the graph. State the domain, range, and asymptote.Mais um parecido para tentar
Exemplo 9Approximating the Solution of a Logarithmic EquationSolve 4ln( x)+1=−2ln( x−1) graphically. Round to the nearest thousandth.Mais um parecido para tentar
Exemplo 10Finding the Vertical Asymptote of a Logarithm GraphWhat is the vertical asymptote of f(x)=−2log3 (x+4)+5?Mais um parecido para tentar
Exemplo 11Finding the Equation from a GraphFind a possible equation for the common logarithmic function graphed in Figure 15. Figure 15Com figuraMais um parecido para tentar

Algebra and Trigonometry6.5 Logarithmic Properties

Exemplo 1Using the Product Rule for LogarithmsExpand log3 ( 30x( 3x+4)).Mais um parecido para tentar
Exemplo 2Using the Quotient Rule for LogarithmsExpand log2 ( (15x(x−1))/((3x+4)(2−x))).Mais um parecido para tentar
Exemplo 3Expanding a Logarithm with PowersExpand log2 x^5.Mais um parecido para tentar
Exemplo 4Rewriting an Expression as a Power before Using the Power RuleExpand log3 ( 25) using the power rule for logs.Mais um parecido para tentar
Exemplo 5Using the Power Rule in ReverseRewrite 4ln(x) using the power rule for logs to a single logarithm with a leading coefficient of 1.Mais um parecido para tentar
Exemplo 6Expanding Logarithms Using Product, Quotient, and Power RulesRewrite ln( (x^4 y)/7) as a sum or difference of logs.Mais um parecido para tentar
Exemplo 7Using the Power Rule for Logarithms to Simplify the Logarithm of a Radical ExpressionExpand log( √x).Mais um parecido para tentar
Exemplo 8Expanding Complex Logarithmic ExpressionsExpand log6 ( (64x^3 ( 4x+1))/(( 2x−1))).Mais um parecido para tentar
Exemplo 9Using the Product and Quotient Rules to Combine LogarithmsWrite log3 ( 5)+log3 ( 8)−log3 ( 2) as a single logarithm.Mais um parecido para tentar
Exemplo 10Condensing Complex Logarithmic ExpressionsCondense log2 ( x^2)+1/2 log2 ( x−1)−3log2 ( ( x+3) ^2).Mais um parecido para tentar
Exemplo 11Rewriting as a Single LogarithmRewrite 2logx−4log(x+5)+1/x log( 3x+5) as a single logarithm.Mais um parecido para tentar
Exemplo 12Applying of the Laws of LogsRecall that, in chemistry, pH=−log[H^+ ]. If the concentration of hydrogen ions in a liquid is doubled, what is the effect on pH?Mais um parecido para tentar
Exemplo 13Changing Logarithmic Expressions to Expressions Involving Only Natural LogsChange log5 3 to a quotient of natural logarithms.Mais um parecido para tentar
Exemplo 14Using the Change-of-Base Formula with a CalculatorEvaluate log2 (10) using the change-of-base formula with a calculator.Mais um parecido para tentar

Algebra and Trigonometry6.6 Exponential and Logarithmic Equations

Exemplo 1Solving an Exponential Equation with a Common BaseSolve 2^(x−1) =2^(2x−4).Mais um parecido para tentar
Exemplo 2Solving Equations by Rewriting Them to Have a Common BaseSolve 8^(x+2) = 16 ^(x+1).Mais um parecido para tentar
Exemplo 3Solving Equations by Rewriting Roots with Fractional Exponents to Have a Common BaseSolve 2^(5x) =√2.Mais um parecido para tentar
Exemplo 4Solving an Equation with Positive and Negative PowersSolve 3^(x+1) =−2.Mais um parecido para tentar
Exemplo 5Solving an Equation Containing Powers of Different BasesSolve 5^(x+2) =4^x.Mais um parecido para tentar
Exemplo 6Solve an Equation of the Form y = AektSolve 100=20e^(2t).Mais um parecido para tentar
Exemplo 7Solving an Equation That Can Be Simplified to the Form y = AektSolve 4e^(2x) +5=12.Mais um parecido para tentar
Exemplo 8Solving Exponential Functions in Quadratic FormSolve e^(2x) −e^x =56.Mais um parecido para tentar
Exemplo 9Using Algebra to Solve a Logarithmic EquationSolve 2lnx+3=7.Mais um parecido para tentar
Exemplo 10Using Algebra Before and After Using the Definition of the Natural LogarithmSolve 2ln(6x)=7.Mais um parecido para tentar
Exemplo 11Using a Graph to Understand the Solution to a Logarithmic EquationSolve lnx=3.Mais um parecido para tentar
Exemplo 12Solving an Equation Using the One-to-One Property of LogarithmsSolve ln(x^2)=ln(2x+3).Mais um parecido para tentar
Exemplo 13Using the Formula for Radioactive Decay to Find the Quantity of a SubstanceHow long will it take for ten percent of a 1000-gram sample of uranium-235 to decay?Mais um parecido para tentar

Algebra and Trigonometry6.7 Exponential and Logarithmic Models

Exemplo 1Graphing Exponential GrowthA population of bacteria doubles every hour. If the culture started with 10 bacteria, graph the population as a function of time.
Exemplo 2Finding the Function that Describes Radioactive DecayThe half-life of carbon-14 is 5,730 years. Express the amount of carbon-14 remaining as a function of time, t.Mais um parecido para tentar
Exemplo 3Finding the Age of a BoneA bone fragment is found that contains 20% of its original carbon-14. To the nearest year, how old is the bone?Mais um parecido para tentar
Exemplo 4Finding a Function That Describes Exponential GrowthAccording to Moore’s Law, the doubling time for the number of transistors that can be put on a computer chip is approximately two years. Give a function that describes this behavior.Mais um parecido para tentar
Exemplo 5Using Newton’s Law of CoolingA cheesecake is taken out of the oven with an ideal internal temperature of 165°F, and is placed into a 35°F refrigerator. After 10 minutes, the cheesecake has cooled to 150°F. If we must wait until the cheesecake…Mais um parecido para tentar
Exemplo 6Using the Logistic-Growth ModelAn influenza epidemic spreads through a population rapidly, at a rate that depends on two factors: The more people who have the flu, the more rapidly it spreads, and also the more uninfected people there are, the…Mais um parecido para tentar
Exemplo 7Choosing a Mathematical ModelDoes a linear, exponential, logarithmic, or logistic model best fit the values listed in Table 1? Find the model, and use a graph to check your choice. x 1 2 3 4 5 6 7 8 9 y 0 1.386 2.197 2.773 3.219 3.584 3.892…Mais um parecido para tentar
Exemplo 8Changing to base eChange the function y=2.5 (3.1) ^x so that this same function is written in the form y=A0 e^(kx).Mais um parecido para tentar

Algebra and Trigonometry6.8 Fitting Exponential Models to Data

Exemplo 1Using Exponential Regression to Fit a Model to DataIn 2007, a university study was published investigating the crash risk of alcohol impaired driving. Data from 2,871 crashes were used to measure the association of a person’s blood alcohol level (BAC) with the risk…Mais um parecido para tentar
Exemplo 2Using Logarithmic Regression to Fit a Model to DataDue to advances in medicine and higher standards of living, life expectancy has been increasing in most developed countries since the beginning of the 20th century. Table 3 shows the average life expectancies, in…Mais um parecido para tentar
Exemplo 3Using Logistic Regression to Fit a Model to DataMobile telephone service has increased rapidly in America since the mid 1990s. Today, almost all residents have cellular service. Table 5 shows the percentage of Americans with cellular service between the years 1995…Mais um parecido para tentar