Expand the Logarithmic Expression log base 4 of 1/4x^2

$\log_{4} (\frac{1}{4} x^{2})$

Rewrite $\log_{4} (\frac{1}{4} x^{2})$ as $\log_{4} (\frac{1}{4}) + \log_{4} (x^{2})$ .

$\log_{4} (\frac{1}{4}) + \log_{4} (x^{2})$

Rewrite $\log_{4} (\frac{1}{4})$ as $\log_{4} (1) - \log_{4} (4)$ .

$\log_{4} (1) - \log_{4} (4) + \log_{4} (x^{2})$

Expand $\log_{4} (x^{2})$ by moving $2$ outside the logarithm.

$\log_{4} (1) - \log_{4} (4) + 2 \log_{4} (x)$

Logarithm base $4$ of $1$ is $0$ .

$0 - \log_{4} (4) + 2 \log_{4} (x)$

Logarithm base $4$ of $4$ is $1$ .

$0 - 1 \cdot 1 + 2 \log_{4} (x)$

Multiply $- 1$ by $1$ .

$0 - 1 + 2 \log_{4} (x)$

Subtract $1$ from $0$ .

$- 1 + 2 \log_{4} (x)$