Solve 14000=7000e^0.08x

$$14000 = 7000 e ^ { 0.08 x }$$

Solve for x

$$x=\frac{25\ln(2)}{2}\approx 8.664339757$$

Steps Using Definition of Logarithm

Divide both sides by 7000.

$$\frac{14000}{7000}=e^{0.08x}$$

Divide 14000 by 7000 to get 2.

$$2=e^{0.08x}$$

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

$$e^{0.08x}=2$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.08x})=\log(2)$$

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

$$0.08x\log(e)=\log(2)$$

Divide both sides by \log(e).

$$0.08x=\frac{\log(2)}{\log(e)}$$

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

$$0.08x=\log_{e}\left(2\right)$$

Divide both sides of the equation by 0.08, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(2)}{0.08}$$

Solve for x (complex solution)

$$x=\frac{25\ln(2)}{2}+i\times 25\pi n_{1}$$

$$n_{1}\in \mathrm{Z}$$