Precalculus Examples

$y = a^{x}$

Step 1

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

$a^{x} = y$

Step 2

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

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

Step 3

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

$x \ln (a) = \ln (y)$

Step 4

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

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Step 4.1

Divide each term in $x \ln (a) = \ln (y)$ by $\ln (a)$ .

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

Step 4.2

Simplify the left side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor.

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

Step 4.2.1.2

Divide $x$ by $1$ .

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