Expand the Logarithmic Expression log base b of 4x^2y

$\log_{b} (4 x^{2} y)$

Step 1

Rewrite $\log_{b} (4 x^{2} y)$ as $\log_{b} (4 x^{2}) + \log_{b} (y)$ .

$\log_{b} (4 x^{2}) + \log_{b} (y)$

Step 2

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

$\log_{b} (4) + \log_{b} (x^{2}) + \log_{b} (y)$

Step 3

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

$\log_{b} (4) + 2 \log_{b} (x) + \log_{b} (y)$

Step 4

Simplify each term.

Rewrite $\log_{b} (4)$ as $\log_{b} (2^{2})$ .

$\log_{b} (2^{2}) + 2 \log_{b} (x) + \log_{b} (y)$

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

$2 \log_{b} (2) + 2 \log_{b} (x) + \log_{b} (y)$