Precalculus Examples

$e^{y + 3} = 7$

Step 1

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

$\ln (e^{y + 3}) = \ln (7)$

Step 2

Expand the left side.

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Step 2.1

Expand $\ln (e^{y + 3})$ by moving $y + 3$ outside the logarithm.

$(y + 3) \ln (e) = \ln (7)$

Step 2.2

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

$(y + 3) \cdot 1 = \ln (7)$

Step 2.3

Multiply $y + 3$ by $1$ .

$y + 3 = \ln (7)$

Step 3

Subtract $3$ from both sides of the equation.

$y = \ln (7) - 3$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \ln (7) - 3$

Decimal Form:

$y = - 1.05408985 \dots$