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Exercises Exponentials and logarithms

Example 4 from Algebra and Trigonometry, 6.6 Exponential and Logarithmic Equations

Solving an Equation with Positive and Negative Powers

Solve $3^{x + 1} = −2.$

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.

Solution
This equation has no solution. There is no real value of $x$ that will make the equation a true statement because any power of a positive number is positive.

Your turn

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

Solve $2^{x} = −100.$

How did it go?

PreviousSolving Equations by Rewriting Roots with Fractional Exponents to Have a Common Base Next Solving an Equation Containing Powers of Different Bases

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 6.6, 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.