Precalculus Examples

$y = a b^{x}$

Step 1

Rewrite the equation as $a b^{x} = y$ .

$a b^{x} = y$

Step 2

Divide each term in $a b^{x} = y$ by $a$ and simplify.

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Step 2.1

Divide each term in $a b^{x} = y$ by $a$ .

$\frac{a b^{x}}{a} = \frac{y}{a}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $a$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{a b^{x}}{a} = \frac{y}{a}$

Step 2.2.1.2

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

$b^{x} = \frac{y}{a}$

Step 3

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

$\ln (b^{x}) = \ln (\frac{y}{a})$

Step 4

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

$x \ln (b) = \ln (\frac{y}{a})$

Step 5

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

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Step 5.1

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

$\frac{x \ln (b)}{\ln (b)} = \frac{\ln (\frac{y}{a})}{\ln (b)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

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

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Step 5.2.1.1

Cancel the common factor.

$\frac{x \ln (b)}{\ln (b)} = \frac{\ln (\frac{y}{a})}{\ln (b)}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{\ln (\frac{y}{a})}{\ln (b)}$