Trigonometry Examples

$\log (64) x = \frac{1}{3}$

Step 1

Divide each term in $\log (64) x = \frac{1}{3}$ by $\log (64)$ .

$\frac{\log (64) x}{\log (64)} = \frac{\frac{1}{3}}{\log (64)}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $\log (64)$ .

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Step 2.1.1

Cancel the common factor.

$\frac{\log (64) x}{\log (64)} = \frac{\frac{1}{3}}{\log (64)}$

Step 2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{3}}{\log (64)}$

Step 3

Simplify the right side.

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Step 3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{3} \cdot \frac{1}{\log (64)}$

Step 3.2

Multiply $\frac{1}{3} \cdot \frac{1}{\log (64)}$ .

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Step 3.2.1

Multiply $\frac{1}{3}$ by $\frac{1}{\log (64)}$ .

$x = \frac{1}{3 \log (64)}$

Step 3.2.2

Simplify $3 \log (64)$ by moving $3$ inside the logarithm.

$x = \frac{1}{\log (64^{3})}$

Step 3.3

Raise $64$ to the power of $3$ .

$x = \frac{1}{\log (262144)}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{\log (262144)}$

Decimal Form:

$x = 0.18455156 \dots$