Precalculus Examples

$\frac{\log (16)}{\frac{4}{3} \cdot \log (10)}$

Step 1

Simplify $\frac{4}{3} \log (10)$ by moving $\frac{4}{3}$ inside the logarithm.

$\frac{\log (16)}{\log (10^{\frac{4}{3}})}$

Step 2

Simplify the denominator.

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Step 2.1

Use logarithm rules to move $\frac{4}{3}$ out of the exponent.

$\frac{\log (16)}{\frac{4}{3} \log (10)}$

Step 2.2

Logarithm base $10$ of $10$ is $1$ .

$\frac{\log (16)}{\frac{4}{3} \cdot 1}$

Step 2.3

Multiply $\frac{4}{3}$ by $1$ .

$\frac{\log (16)}{\frac{4}{3}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\log (16) \frac{3}{4}$

Step 4

Multiply $\log (16) \frac{3}{4}$ .

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Step 4.1

Reorder $\log (16)$ and $\frac{3}{4}$ .

$\frac{3}{4} \log (16)$

Step 4.2

Simplify $\frac{3}{4} \log (16)$ by moving $\frac{3}{4}$ inside the logarithm.

$\log (16^{\frac{3}{4}})$

Step 5

Simplify the expression.

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Step 5.1

Rewrite $16$ as $2^{4}$ .

$\log ({(2^{4})}^{\frac{3}{4}})$

Step 5.2

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

$\log (2^{4 (\frac{3}{4})})$

Step 6

Cancel the common factor of $4$ .

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Step 6.1

Cancel the common factor.

$\log (2^{4 (\frac{3}{4})})$

Step 6.2

Rewrite the expression.

$\log (2^{3})$

Step 7

Raise $2$ to the power of $3$ .

$\log (8)$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\log (8)$

Decimal Form:

$0.90308998 \dots$