Chapter 9 - Section 9.3 - Logarithmic Functions - 9.3 Exercises - Page 606: 58

{9}

For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$. Therefore, $log_{\sqrt2}(\sqrt2)^{9}=x$ means the same as $(\sqrt2) ^{x}=(\sqrt2)^{9}$. We know that $x=9$, because $(\sqrt2)^{9}=(\sqrt2)^{9}$.