Calculus Examples

$\log_{b} (2 x^{2} y^{3})$

Step 1

Rewrite $\log_{b} (2 x^{2} y^{3})$ as $\log_{b} (2 x^{2}) + \log_{b} (y^{3})$ .

$\log_{b} (2 x^{2}) + \log_{b} (y^{3})$

Step 2

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

$\log_{b} (2) + \log_{b} (x^{2}) + \log_{b} (y^{3})$

Step 3

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

$\log_{b} (2) + 2 \log_{b} (x) + \log_{b} (y^{3})$

Step 4

Expand $\log_{b} (y^{3})$ by moving $3$ outside the logarithm.

$\log_{b} (2) + 2 \log_{b} (x) + 3 \log_{b} (y)$