Precalculus Examples

$4 \log_{5} (652)$

Step 1

Rewrite $\log_{5} (652)$ as $\log_{5} (2^{2} \cdot 163)$ .

$4 \log_{5} (2^{2} \cdot 163)$

Step 2

Rewrite $\log_{5} (2^{2} \cdot 163)$ as $\log_{5} (2^{2}) + \log_{5} (163)$ .

$4 (\log_{5} (2^{2}) + \log_{5} (163))$

Step 3

Expand $\log_{5} (2^{2})$ by moving $2$ outside the logarithm.

$4 (2 \log_{5} (2) + \log_{5} (163))$

Step 4

Apply the distributive property.

$4 (2 \log_{5} (2)) + 4 \log_{5} (163)$

Step 5

Multiply $2$ by $4$ .

$8 \log_{5} (2) + 4 \log_{5} (163)$