Solve e^7x=21

$$e ^ { 7 x } = 21$$

Solve for x

$$x=\frac{\ln(21)}{7}\approx 0.434931777$$

Steps Using Definition of Logarithm

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

$$e^{7x}=21$$

Take the logarithm of both sides of the equation.

$$\log(e^{7x})=\log(21)$$

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

$$7x\log(e)=\log(21)$$

Divide both sides by \log(e).

$$7x=\frac{\log(21)}{\log(e)}$$

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

$$7x=\log_{e}\left(21\right)$$

Divide both sides by 7.

$$x=\frac{\ln(21)}{7}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{7}+\frac{\ln(21)}{7}$$

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