Solve 20000=2000e^0.195x

$$20000 = 2000 { e }^{ 0.195x }$$

Solve for x

$$x=\frac{200\ln(10)}{39}\approx 11.808128682$$

Steps Using Definition of Logarithm

Divide both sides by 2000.

$$\frac{20000}{2000}=e^{0.195x}$$

Divide 20000 by 2000 to get 10.

$$10=e^{0.195x}$$

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

$$e^{0.195x}=10$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.195x})=\log(10)$$

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

$$0.195x\log(e)=\log(10)$$

Divide both sides by \log(e).

$$0.195x=\frac{\log(10)}{\log(e)}$$

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

$$0.195x=\log_{e}\left(10\right)$$

Divide both sides of the equation by 0.195, which is the same as multiplying both sides by the reciprocal of the fraction.

$$x=\frac{\ln(10)}{0.195}$$

Solve for x (complex solution)

$$x=\frac{i\times 400\pi n_{1}}{39}+\frac{200\ln(10)}{39}$$

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