Precalculus Examples

$\log_{5} (\ln (25))$

Step 1

Rewrite $\ln (25)$ as $\ln (5^{2})$ .

$\log_{5} (\ln (5^{2}))$

Step 2

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

$\log_{5} (2 \ln (5))$

Step 3

Rewrite $\log_{5} (2 \ln (5))$ as $\log_{5} (2) + \log_{5} (\ln (5))$ .

$\log_{5} (2) + \log_{5} (\ln (5))$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log_{5} (2) + \log_{5} (\ln (5))$

Decimal Form:

$0.72636053 \dots$