Solve e^0.14t=38

$$e ^ { 0.14 t } = 38$$

Solve for t

$$t=\frac{50\ln(38)}{7}\approx 25.982758284$$

Steps Using Definition of Logarithm

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

$$e^{0.14t}=38$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.14t})=\log(38)$$

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

$$0.14t\log(e)=\log(38)$$

Divide both sides by \log(e).

$$0.14t=\frac{\log(38)}{\log(e)}$$

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

$$0.14t=\log_{e}\left(38\right)$$

Divide both sides of the equation by 0.14, which is the same as multiplying both sides by the reciprocal of the fraction.

$$t=\frac{\ln(38)}{0.14}$$