Precalculus Examples

$e^{y + 4} = 4$

Step 1

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

$\ln (e^{y + 4}) = \ln (4)$

Step 2

Expand the left side.

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Step 2.1

Expand $\ln (e^{y + 4})$ by moving $y + 4$ outside the logarithm.

$(y + 4) \ln (e) = \ln (4)$

Step 2.2

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

$(y + 4) \cdot 1 = \ln (4)$

Step 2.3

Multiply $y + 4$ by $1$ .

$y + 4 = \ln (4)$

Step 3

Subtract $4$ from both sides of the equation.

$y = \ln (4) - 4$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \ln (4) - 4$

Decimal Form:

$y = - 2.61370563 \dots$