Precalculus Examples

$\log (2^{2015} \cdot 175^{175})$

Step 1

Rewrite $\log (2^{2015} \cdot 175^{175})$ as $\log (2^{2015}) + \log (175^{175})$ .

$\log (2^{2015}) + \log (175^{175})$

Step 2

Expand $\log (2^{2015})$ by moving $2015$ outside the logarithm.

$2015 \log (2) + \log (175^{175})$

Step 3

Expand $\log (175^{175})$ by moving $175$ outside the logarithm.

$2015 \log (2) + 175 \log (175)$

Step 4

Rewrite $\log (175)$ as $\log (5^{2} \cdot 7)$ .

$2015 \log (2) + 175 \log (5^{2} \cdot 7)$

Step 5

Rewrite $\log (5^{2} \cdot 7)$ as $\log (5^{2}) + \log (7)$ .

$2015 \log (2) + 175 (\log (5^{2}) + \log (7))$

Step 6

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

$2015 \log (2) + 175 (2 \log (5) + \log (7))$

Step 7

Apply the distributive property.

$2015 \log (2) + 175 (2 \log (5)) + 175 \log (7)$

Step 8

Multiply $2$ by $175$ .

$2015 \log (2) + 350 \log (5) + 175 \log (7)$