Precalculus Examples

$e^{y - 9} = 6$

Step 1

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

$\ln (e^{y - 9}) = \ln (6)$

Step 2

Expand the left side.

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Step 2.1

Expand $\ln (e^{y - 9})$ by moving $y - 9$ outside the logarithm.

$(y - 9) \ln (e) = \ln (6)$

Step 2.2

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

$(y - 9) \cdot 1 = \ln (6)$

Step 2.3

Multiply $y - 9$ by $1$ .

$y - 9 = \ln (6)$

Step 3

Add $9$ to both sides of the equation.

$y = \ln (6) + 9$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \ln (6) + 9$

Decimal Form:

$y = 10.79175946 \dots$