Algebra Examples

$a^{\frac{b}{4}} = 16$

Step 1

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (a^{\frac{b}{4}}) = \ln (16)$

Step 2

Expand the left side.

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Step 2.1

Expand $\ln (a^{\frac{b}{4}})$ by moving $\frac{b}{4}$ outside the logarithm.

$\frac{b}{4} \ln (a) = \ln (16)$

Step 2.2

Combine $\frac{b}{4}$ and $\ln (a)$ .

$\frac{b \ln (a)}{4} = \ln (16)$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{b \ln (a)}{4} = 4 \ln (16)$

Step 4

Simplify the left side.

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Step 4.1

Cancel the common factor of $4$ .

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Step 4.1.1

Cancel the common factor.

$4 \frac{b \ln (a)}{4} = 4 \ln (16)$

Step 4.1.2

Rewrite the expression.

$b \ln (a) = 4 \ln (16)$

Step 5

Divide each term in $b \ln (a) = 4 \ln (16)$ by $\ln (a)$ and simplify.

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Step 5.1

Divide each term in $b \ln (a) = 4 \ln (16)$ by $\ln (a)$ .

$\frac{b \ln (a)}{\ln (a)} = \frac{4 \ln (16)}{\ln (a)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (a)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{b \ln (a)}{\ln (a)} = \frac{4 \ln (16)}{\ln (a)}$

Step 5.2.1.2

Divide $b$ by $1$ .

$b = \frac{4 \ln (16)}{\ln (a)}$