Algebra Examples

$5 \ln (2) + 3 \ln (x) - \frac{1}{2} \ln (x + 9)$

Step 1

Simplify each term.

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Step 1.1

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

$\ln (2^{5}) + 3 \ln (x) - \frac{1}{2} \cdot \ln (x + 9)$

Step 1.2

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

$\ln (32) + 3 \ln (x) - \frac{1}{2} \cdot \ln (x + 9)$

Step 1.3

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

$\ln (32) + \ln (x^{3}) - \frac{1}{2} \cdot \ln (x + 9)$

Step 1.4

Multiply $- \frac{1}{2} \ln (x + 9)$ .

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Step 1.4.1

Reorder $\ln (x + 9)$ and $\frac{1}{2}$ .

$\ln (32) + \ln (x^{3}) - (\frac{1}{2} \ln (x + 9))$

Step 1.4.2

Simplify $\frac{1}{2} \ln (x + 9)$ by moving $\frac{1}{2}$ inside the logarithm.

$\ln (32) + \ln (x^{3}) - \ln ({(x + 9)}^{\frac{1}{2}})$

Step 2

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

$\ln (32 x^{3}) - \ln ({(x + 9)}^{\frac{1}{2}})$

Step 3

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

$\ln (\frac{32 x^{3}}{{(x + 9)}^{\frac{1}{2}}})$