The value of $\log_{\sqrt{2}}(32)$ is

Explanation

Let $\log_{\sqrt{2}}(32) = \log_{\sqrt{2}}(2)^5$ $= \log_{\sqrt{2}}(\sqrt{2}.\sqrt{2})^5$ $= \log_{\sqrt{2}}(\sqrt{2})^1$ $\log_{\sqrt{2}}\sqrt{2}$ $(\because \log_x x = 1) = 10 \times 1 = 10$