Precalculus Examples

$\frac{1}{3} \cdot \log (8) + \log (15)$

Step 1

Simplify each term.

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Step 1.1

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

$\log (8^{\frac{1}{3}}) + \log (15)$

Step 1.2

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

$\log ({(2^{3})}^{\frac{1}{3}}) + \log (15)$

Step 1.3

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

$\log (2^{3 (\frac{1}{3})}) + \log (15)$

Step 1.4

Cancel the common factor of $3$ .

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Step 1.4.1

Cancel the common factor.

$\log (2^{3 (\frac{1}{3})}) + \log (15)$

Step 1.4.2

Rewrite the expression.

$\log (2^{1}) + \log (15)$

Step 1.5

Evaluate the exponent.

$\log (2) + \log (15)$

Step 2

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

$\log (2 \cdot 15)$

Step 3

Multiply $2$ by $15$ .

$\log (30)$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\log (30)$

Decimal Form:

$1.47712125 \dots$