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Exercises Exponentials and logarithms

Example 1 from Algebra and Trigonometry, 6.3 Logarithmic Functions

Converting from Logarithmic Form to Exponential Form

Write the following logarithmic equations in exponential form.

ⓐ $\log_{6} (\sqrt{6}) = \frac{1}{2}$
ⓑ $\log_{3} (9) = 2$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
First, identify the values of $b, y, and x .$ Then, write the equation in the form $b^{y} = x .$
- ⓐ $\log_{6} (\sqrt{6}) = \frac{1}{2}$
  Here, $b = 6, y = \frac{1}{2}, and x = \sqrt{6.}$ Therefore, the equation $\log_{6} (\sqrt{6}) = \frac{1}{2}$ is equivalent to $6^{\frac{1}{2}} = \sqrt{6} .$
- ⓑ $\log_{3} (9) = 2$
  Here, $b = 3, y = 2, and x = 9.$ Therefore, the equation $\log_{3} (9) = 2$ is equivalent to $3^{2} = 9.$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Write the following logarithmic equations in exponential form.

ⓐ $\log_{10} (1, 000, 000) = 6$
ⓑ $\log_{5} (25) = 2$

How did it go?

PreviousWriting a Function from a Description Next Converting from Exponential Form to Logarithmic Form

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 6.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.