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Exercises Exponentials and logarithms

Example 10 from Algebra and Trigonometry, 6.6 Exponential and Logarithmic Equations

Using Algebra Before and After Using the Definition of the Natural Logarithm

Solve $2 \ln (6 x) = 7.$

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
$\begin{array}{l} 2 \ln (6 x) = 7 \\ \ln (6 x) = \frac{7}{2} & Divide by 2 . \\ 6 x = e^{(\frac{7}{2})} & Use the definition of \ln . \\ x = \frac{1}{6} e^{(\frac{7}{2})} & Divide by 6 . \end{array}$

Your turn

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

Solve $2 \ln (x + 1) = 10.$

How did it go?

PreviousUsing Algebra to Solve a Logarithmic Equation Next Using a Graph to Understand the Solution to a Logarithmic Equation

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.