Solve 2=e^t/20

$$2 = e ^ { t / 20 }$$

Solve for t

$$t=20\ln(2)\approx 13.862943611$$

Steps Using Definition of Logarithm

Swap sides so that all variable terms are on the left hand side.

$$e^{\frac{t}{20}}=2$$

Use the rules of exponents and logarithms to solve the equation.

$$e^{\frac{1}{20}t}=2$$

Take the logarithm of both sides of the equation.

$$\log(e^{\frac{1}{20}t})=\log(2)$$

The logarithm of a number raised to a power is the power times the logarithm of the number.

$$\frac{1}{20}t\log(e)=\log(2)$$

Divide both sides by \log(e).

$$\frac{1}{20}t=\frac{\log(2)}{\log(e)}$$

By the change-of-base formula \frac{\log(a)}{\log(b)}=\log_{b}\left(a\right).

$$\frac{1}{20}t=\log_{e}\left(2\right)$$

Multiply both sides by 20.

$$t=\frac{\ln(2)}{\frac{1}{20}}$$