48. Solve the following logarithm

Name: 48. Solve the following logarithm
Uploaded: 2011-02-08
Description: Solution Suppose$$log_9 \sqrt{3}=x$$That means\begin{align}9^x = \sqrt{3}\\9^x = 3^{\frac{1}{2}}\\(3^2)^x = 3^{\frac{1}{2}}\\3^{2x} = 3^{\frac{1}{2}}\\2x = \frac{1}{2}\\x=\frac{1}{4}\end{align}

$$\begin{array}{lcl} 48.\;What\;is\;\log_9 \sqrt{3}?\\ \\ (F)\; 0.4\\ (G)\; 1.0\\ (H)\; 0.125\\ (J)\; 0.5\\ (K)\; 0.25\\ \end{array}$$

Suppose

$$log_9 \sqrt{3}=x$$

That means

\begin{align}
9^x = \sqrt{3}\\
9^x = 3^{\frac{1}{2}}\\
(3^2)^x = 3^{\frac{1}{2}}\\
3^{2x} = 3^{\frac{1}{2}}\\
2x = \frac{1}{2}\\
x=\frac{1}{4}
\end{align}