Precalculus Examples

$\frac{2}{3} \cdot \ln (8) - \ln (5 - 1)$

Step 1

Simplify each term.

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Step 1.1

Simplify $\frac{2}{3} \ln (8)$ by moving $\frac{2}{3}$ inside the logarithm.

$\ln (8^{\frac{2}{3}}) - \ln (5 - 1)$

Step 1.2

Rewrite $8$ as $2^{3}$ .

$\ln ({(2^{3})}^{\frac{2}{3}}) - \ln (5 - 1)$

Step 1.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\ln (2^{3 (\frac{2}{3})}) - \ln (5 - 1)$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Cancel the common factor.

$\ln (2^{3 (\frac{2}{3})}) - \ln (5 - 1)$

Step 1.4.2

Rewrite the expression.

$\ln (2^{2}) - \ln (5 - 1)$

Step 1.5

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

$\ln (4) - \ln (5 - 1)$

Step 1.6

Subtract $1$ from $5$ .

$\ln (4) - \ln (4)$

Step 2

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

$\ln (\frac{4}{4})$

Step 3

Divide $4$ by $4$ .

$\ln (1)$

Step 4

The natural logarithm of $1$ is $0$ .

$0$