Solve e^99x=4879

$$e ^ { 99 x } = 4879$$

Solve for x

$$x=\frac{\ln(4879)}{99}\approx 0.085784804$$

Steps Using Definition of Logarithm

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

$$e^{99x}=4879$$

Take the logarithm of both sides of the equation.

$$\log(e^{99x})=\log(4879)$$

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

$$99x\log(e)=\log(4879)$$

Divide both sides by \log(e).

$$99x=\frac{\log(4879)}{\log(e)}$$

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

$$99x=\log_{e}\left(4879\right)$$

Divide both sides by 99.

$$x=\frac{\ln(4879)}{99}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{99}+\frac{\ln(4879)}{99}$$

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