Calculus Examples

$\ln (5) + 5 \ln (3)$

Step 1

Simplify each term.

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Step 1.1

Simplify $5 \ln (3)$ by moving $5$ inside the logarithm.

$\ln (5) + \ln (3^{5})$

Step 1.2

Raise $3$ to the power of $5$ .

$\ln (5) + \ln (243)$

Step 2

Use the product property of logarithms, $\log_{b} (x) + \log_{b} (y) = \log_{b} (x y)$ .

$\ln (5 \cdot 243)$

Step 3

Multiply $5$ by $243$ .

$\ln (1215)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\ln (1215)$

Decimal Form:

$7.10249935 \dots$