Solve 8000000=100e^.01t

$$8000000 = 100 e ^ { .01 t }$$

Solve for t

$$t=100\ln(80000)\approx 1128.978191366$$

Steps Using Definition of Logarithm

Divide both sides by 100.

$$\frac{8000000}{100}=e^{0.01t}$$

Divide 8000000 by 100 to get 80000.

$$80000=e^{0.01t}$$

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

$$e^{0.01t}=80000$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.01t})=\log(80000)$$

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

$$0.01t\log(e)=\log(80000)$$

Divide both sides by \log(e).

$$0.01t=\frac{\log(80000)}{\log(e)}$$

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

$$0.01t=\log_{e}\left(80000\right)$$

Multiply both sides by 100.

$$t=\frac{\ln(80000)}{0.01}$$