Algebra Examples

$a \cdot b^{c} = d$

Step 1

Divide each term in $a \cdot b^{c} = d$ by $a$ and simplify.

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Step 1.1

Divide each term in $a \cdot b^{c} = d$ by $a$ .

$\frac{a \cdot b^{c}}{a} = \frac{d}{a}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $a$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{a \cdot b^{c}}{a} = \frac{d}{a}$

Step 1.2.1.2

Divide $b^{c}$ by $1$ .

$b^{c} = \frac{d}{a}$

Step 2

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

$\ln (b^{c}) = \ln (\frac{d}{a})$

Step 3

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

$c \ln (b) = \ln (\frac{d}{a})$

Step 4

Divide each term in $c \ln (b) = \ln (\frac{d}{a})$ by $\ln (b)$ and simplify.

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Step 4.1

Divide each term in $c \ln (b) = \ln (\frac{d}{a})$ by $\ln (b)$ .

$\frac{c \ln (b)}{\ln (b)} = \frac{\ln (\frac{d}{a})}{\ln (b)}$

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor.

$\frac{c \ln (b)}{\ln (b)} = \frac{\ln (\frac{d}{a})}{\ln (b)}$

Step 4.2.1.2

Divide $c$ by $1$ .

$c = \frac{\ln (\frac{d}{a})}{\ln (b)}$