Solve 20000=7000{(e)^.20x}

$$20000=7000 {(e)^{ .20x }}$$

Solve for x

$$x=\ln(\frac{3200000}{16807})\approx 5.249110622$$

Steps Using Definition of Logarithm

Divide both sides by 7000.

$$\frac{20000}{7000}=e^{0.2x}$$

Reduce the fraction \frac{20000}{7000} to lowest terms by extracting and canceling out 1000.

$$\frac{20}{7}=e^{0.2x}$$

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

$$e^{0.2x}=\frac{20}{7}$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.2x})=\log(\frac{20}{7})$$

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

$$0.2x\log(e)=\log(\frac{20}{7})$$

Divide both sides by \log(e).

$$0.2x=\frac{\log(\frac{20}{7})}{\log(e)}$$

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

$$0.2x=\log_{e}\left(\frac{20}{7}\right)$$

Multiply both sides by 5.

$$x=\frac{\ln(\frac{20}{7})}{0.2}$$

Solve for x (complex solution)

$$x=\ln(\frac{3200000}{16807})+i\times 10\pi n_{1}$$

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