Solve 19000=95000e^0.01x

$$19000 = 95000 e ^ { 0.01 x }$$

Solve for x

$$x=-100\ln(5)\approx -160.943791243$$

Steps Using Definition of Logarithm

Divide both sides by 95000.

$$\frac{19000}{95000}=e^{0.01x}$$

Reduce the fraction \frac{19000}{95000} to lowest terms by extracting and canceling out 19000.

$$\frac{1}{5}=e^{0.01x}$$

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

$$e^{0.01x}=\frac{1}{5}$$

Take the logarithm of both sides of the equation.

$$\log(e^{0.01x})=\log(\frac{1}{5})$$

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

$$0.01x\log(e)=\log(\frac{1}{5})$$

Divide both sides by \log(e).

$$0.01x=\frac{\log(\frac{1}{5})}{\log(e)}$$

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

$$0.01x=\log_{e}\left(\frac{1}{5}\right)$$

Multiply both sides by 100.

$$x=-\frac{\ln(5)}{0.01}$$

Solve for x (complex solution)

$$x=-100\ln(5)+i\times 200\pi n_{1}$$

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