Algebra Examples

$\ln (30) + 2 \ln (5) - \ln (15)$

Step 1

Use the quotient property of logarithms, $\log_{b} (x) - \log_{b} (y) = \log_{b} (\frac{x}{y})$ .

$2 \ln (5) + \ln (\frac{30}{15})$

Step 2

Simplify each term.

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Step 2.1

Simplify $2 \ln (5)$ by moving $2$ inside the logarithm.

$\ln (5^{2}) + \ln (\frac{30}{15})$

Step 2.2

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

$\ln (25) + \ln (\frac{30}{15})$

Step 2.3

Divide $30$ by $15$ .

$\ln (25) + \ln (2)$

Step 3

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

$\ln (25 \cdot 2)$

Step 4

Multiply $25$ by $2$ .

$\ln (50)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\ln (50)$

Decimal Form:

$3.91202300 \dots$