College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.6 - Logarithmic and Exponential Equations - 6.6 Assess Your Understanding - Page 465: 50

Answer

$\displaystyle \{\frac{\log 5-\log 2}{\log 2+2\log 5}\}$ or $\{0.234\}$

Work Step by Step

... Apply $\log$(...) to both sides $\log 2^{x+1}=\log 5^{1-2x}$ $\quad $...Apply$: \quad \log_{a}M^{r}=r\log_{a}M\quad $ $(x+1)\log 2=(1-2x)\log 5\quad $... isolate x $x\log 2+\log 2=\log 5-2x\log 5$ $x\log 2+2x\log 5==\log 5-\log 2$ $x(\log 2+2\log 5)=\log 5-\log 2$ $x=\displaystyle \frac{\log 5-\log 2}{\log 2+2\log 5}\approx 0.234$ Solution set: $\displaystyle \{\frac{\log 5-\log 2}{\log 2+2\log 5}\}$ or $\{0.234\}$
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.