Answer
$x=±\sqrt {\frac{\ln(45)}{\ln(3)}}$
Work Step by Step
Use the natural log on both sides to solve for $x$.
$3^{x^2}=45$
$\ln(3^{x^2})=\ln(45)$
$x^2\ln(3)=\ln(45)$
$x^2=\frac{\ln(45)}{\ln(3)}$
$x=±\sqrt {\frac{\ln(45)}{\ln(3)}}$
College Algebra (6th Edition)
by Blitzer, Robert F.
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 - Page 490: 97
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