Precalculus Examples

$\log_{b} (x^{3} y^{7} z)$

Step 1

Rewrite $\log_{b} (x^{3} y^{7} z)$ as $\log_{b} (x^{3} y^{7}) + \log_{b} (z)$ .

$\log_{b} (x^{3} y^{7}) + \log_{b} (z)$

Step 2

Rewrite $\log_{b} (x^{3} y^{7})$ as $\log_{b} (x^{3}) + \log_{b} (y^{7})$ .

$\log_{b} (x^{3}) + \log_{b} (y^{7}) + \log_{b} (z)$

Step 3

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

$3 \log_{b} (x) + \log_{b} (y^{7}) + \log_{b} (z)$

Step 4

Expand $\log_{b} (y^{7})$ by moving $7$ outside the logarithm.

$3 \log_{b} (x) + 7 \log_{b} (y) + \log_{b} (z)$