### Home > PC > Chapter 3 > Lesson 3.3.1 > Problem3-109

3-109.

Show that $\log_4x=\frac{1}{2}\log_2x$. Start with $y=\log_4x$ and change to exponent form.

Start on the left side and set it equal to $y$.

$\log_4x=y$

Now take the $\log_2x$ on both sides.

$\log_22^{2y}=\log_2x$

$2y = \text{log}_{2}{x}$

$y = \frac{1}{2}\text{log}_{2}{x}$