Solve for t 2.75e^t=38.6

$2.75 e^{t} = 38.6$

Divide each term in $2.75 e^{t} = 38.6$ by $2.75$ and simplify.

Divide each term in $2.75 e^{t} = 38.6$ by $2.75$ .

$\frac{2.75 e^{t}}{2.75} = \frac{38.6}{2.75}$

Simplify the left side.

Cancel the common factor of $2.75$ .

Cancel the common factor.

$\frac{2.75 e^{t}}{2.75} = \frac{38.6}{2.75}$

Divide $e^{t}$ by $1$ .

$e^{t} = \frac{38.6}{2.75}$

Simplify the right side.

Divide $38.6$ by $2.75$ .

$e^{t} = 14.0\overline{36}$

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

$\ln (e^{t}) = \ln (14.0\overline{36})$

Expand the left side.

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

$t \ln (e) = \ln (14.0\overline{36})$

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

$t \cdot 1 = \ln (14.0\overline{36})$

Multiply $t$ by $1$ .

$t = \ln (14.0\overline{36})$

The result can be shown in multiple forms.

Exact Form:

$t = \ln (14.0\overline{36})$

Decimal Form:

$t = 2.64165136 \dots$