Precalculus Examples

$- \frac{1}{3} \cdot \log (8)$

Step 1

Multiply $- \frac{1}{3} \log (8)$ .

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Step 1.1

Reorder $\log (8)$ and $\frac{1}{3}$ .

$- (\frac{1}{3} \log (8))$

Step 1.2

Simplify $\frac{1}{3} \log (8)$ by moving $\frac{1}{3}$ inside the logarithm.

$- \log (8^{\frac{1}{3}})$

Step 2

Simplify the expression.

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Step 2.1

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

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

Step 2.2

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

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$- \log (2^{1})$

Step 4

Evaluate the exponent.

$- \log (2)$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \log (2)$

Decimal Form:

$- 0.30102999 \dots$