Precalculus Examples

$\log_{5} ({(2^{5} \cdot 11)}^{3})$

Step 1

Expand $\log_{5} ({(2^{5} \cdot 11)}^{3})$ by moving $3$ outside the logarithm.

$3 \log_{5} (2^{5} \cdot 11)$

Step 2

Raise $2$ to the power of $5$ .

$3 \log_{5} (32 \cdot 11)$

Step 3

Multiply $32$ by $11$ .

$3 \log_{5} (352)$

Step 4

Rewrite $\log_{5} (352)$ as $\log_{5} (2^{5} \cdot 11)$ .

$3 \log_{5} (2^{5} \cdot 11)$

Step 5

Rewrite $\log_{5} (2^{5} \cdot 11)$ as $\log_{5} (2^{5}) + \log_{5} (11)$ .

$3 (\log_{5} (2^{5}) + \log_{5} (11))$

Step 6

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

$3 (5 \log_{5} (2) + \log_{5} (11))$

Step 7

Apply the distributive property.

$3 (5 \log_{5} (2)) + 3 \log_{5} (11)$

Step 8

Multiply $5$ by $3$ .

$15 \log_{5} (2) + 3 \log_{5} (11)$