Algebra 2 Common Core

Published by Prentice Hall
ISBN 10: 0133186024
ISBN 13: 978-0-13318-602-4

Chapter 11 - Probability and Statistics - 11-4 Conditional Probability - Practice and Problem-Solving Exercises - Page 702: 43



Work Step by Step

Taking the logarithm of both sides, the given equation, $ 4^{2x}=10 ,$ is equivalent to \begin{align*} \log4^{2x}=\log10 .\end{align*} Using the properties of logarithms, the equation above is equivalent to \begin{align*} \log4^{2x}&=1 &\left(\text{use }\log10=1 \right) \\ 2x\log4&=1 &\left(\text{use }\log_ba^x=x\log_ba \right) \\\\ \dfrac{2x\log4}{2\log4}&=\dfrac{1}{2\log4} \\\\ x&=\dfrac{1}{2\log4} \\\\ x&\approx0.830 .\end{align*} Hence, the solution is $ x\approx0.830 .$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.