Precalculus Examples

$e^{y - 8} = 2$

Step 1

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

$\ln (e^{y - 8}) = \ln (2)$

Step 2

Expand the left side.

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Step 2.1

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

$(y - 8) \ln (e) = \ln (2)$

Step 2.2

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

$(y - 8) \cdot 1 = \ln (2)$

Step 2.3

Multiply $y - 8$ by $1$ .

$y - 8 = \ln (2)$

Step 3

Add $8$ to both sides of the equation.

$y = \ln (2) + 8$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \ln (2) + 8$

Decimal Form:

$y = 8.69314718 \dots$