Solve 2=e^0.06t

$$2 = e ^ { 0.06 t }$$

Solve for t

$$t=\frac{50\ln(2)}{3}\approx 11.552453009$$

Steps Using Definition of Logarithm

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

$$e^{0.06t}=2$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.06t})=\log(2)$$

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

$$0.06t\log(e)=\log(2)$$

Divide both sides by \log(e).

$$0.06t=\frac{\log(2)}{\log(e)}$$

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

$$0.06t=\log_{e}\left(2\right)$$

Divide both sides of the equation by 0.06, which is the same as multiplying both sides by the reciprocal of the fraction.

$$t=\frac{\ln(2)}{0.06}$$