Solve for t 7*e^(0.1t)=47

$7 \cdot e^{0.1 t} = 47$

Divide each term in $(7 \cdot e^{0.1 t}) = 47$ by $7$ and simplify.

Divide each term in $(7 \cdot e^{0.1 t}) = 47$ by $7$ .

$\frac{(7 \cdot e^{0.1 t})}{7} = \frac{47}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 \cdot e^{0.1 t}}{7} = \frac{47}{7}$

Divide $e^{0.1 t}$ by $1$ .

$e^{0.1 t} = \frac{47}{7}$

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

$\ln (e^{0.1 t}) = \ln (\frac{47}{7})$

Expand the left side.

Expand $\ln (e^{0.1 t})$ by moving $0.1 t$ outside the logarithm.

$0.1 t \ln (e) = \ln (\frac{47}{7})$

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

$0.1 t \cdot 1 = \ln (\frac{47}{7})$

Multiply $0.1$ by $1$ .

$0.1 t = \ln (\frac{47}{7})$

Divide each term in $0.1 t = \ln (\frac{47}{7})$ by $0.1$ and simplify.

Divide each term in $0.1 t = \ln (\frac{47}{7})$ by $0.1$ .

$\frac{0.1 t}{0.1} = \frac{\ln (\frac{47}{7})}{0.1}$

Simplify the left side.

Cancel the common factor of $0.1$ .

Cancel the common factor.

$\frac{0.1 t}{0.1} = \frac{\ln (\frac{47}{7})}{0.1}$

Divide $t$ by $1$ .

$t = \frac{\ln (\frac{47}{7})}{0.1}$

Simplify the right side.

Replace $e$ with an approximation.

$t = \frac{\log_{2.71828182} (\frac{47}{7})}{0.1}$

Divide $47$ by $7$ .

$t = \frac{\log_{2.71828182} (6.\overline{714285})}{0.1}$

Log base $2.71828182$ of $6.\overline{714285}$ is approximately $1.90423745$ .

$t = \frac{1.90423745}{0.1}$

Divide $1.90423745$ by $0.1$ .

$t = 19.04237452$