College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 4 - Exponential and Logarithmic Functions - Exercise Set 4.4: 93

Answer

$x=\frac{1}{2}$

Work Step by Step

Use the law of exponents ($b^n\times b^m=b^{n+m}$) to add the exponents together. Then rewrite $125$ to have base $5$. With the bases equal, set the exponents equal to each other and solve. $5^{2x}\times5^{4x}=125$ $5^{6x}=125$ $5^{6x}=5^3$ $6x=3$ $x=\frac{1}{2}$
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