Precalculus Examples

$e^{4 x - 8} = 1$

Step 1

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

$\ln (e^{4 x - 8}) = \ln (1)$

Step 2

Expand the left side.

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Step 2.1

Expand $\ln (e^{4 x - 8})$ by moving $4 x - 8$ outside the logarithm.

$(4 x - 8) \ln (e) = \ln (1)$

Step 2.2

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

$(4 x - 8) \cdot 1 = \ln (1)$

Step 2.3

Multiply $4 x - 8$ by $1$ .

$4 x - 8 = \ln (1)$

Step 3

Simplify the right side.

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Step 3.1

The natural logarithm of $1$ is $0$ .

$4 x - 8 = 0$

Step 4

Add $8$ to both sides of the equation.

$4 x = 8$

Step 5

Divide each term in $4 x = 8$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 x = 8$ by $4$ .

$\frac{4 x}{4} = \frac{8}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{8}{4}$

Step 5.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $8$ by $4$ .

$x = 2$