College Algebra (10th Edition)

$3^x = 5$ or $3^x=-5$
Note that $9=3^2$. Thus, $9^x=25$ is equivalent to: $(3^2)^x=25$ Use the rule $(a^m)^n=a^{mn}$ to obtain: $3^{2x} = 25$ Use the rule $a^{mn} = (a^m)^n$ to obtain: $(3^x)^2=25$ Take the square root of both sides to obtain: $\sqrt{(3^x)^2}=\pm \sqrt{25} \\3^x = \pm \sqrt{5^2} \\3^x = \pm 5$ Thus, $3^x = 5$ or $3^x=-5$