Precalculus Examples

$\ln (e^{12 x}) = 60$

Step 1

Expand $\ln (e^{12 x})$ .

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Step 1.1

Expand $\ln (e^{12 x})$ by moving $12 x$ outside the logarithm.

$12 x \ln (e)$

Step 1.2

The natural logarithm of $e$ is $1$ .

$12 x \cdot 1$

Step 1.3

Multiply $12$ by $1$ .

$12 x$

Step 2

The expanded equation is $12 x = 60$ .

$12 x = 60$

Step 3

Divide each term in $12 x = 60$ by $12$ and simplify.

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Step 3.1

Divide each term in $12 x = 60$ by $12$ .

$\frac{12 x}{12} = \frac{60}{12}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $12$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{12 x}{12} = \frac{60}{12}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{60}{12}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $60$ by $12$ .

$x = 5$