Solve e^x=8.4

$${ e }^{ x } =8.4$$

Solve for x

$$x=\ln(8.4)\approx 2.128231706$$

Steps Using Definition of Logarithm

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

$$e^{x}=8.4$$

Take the logarithm of both sides of the equation.

$$\log(e^{x})=\log(8.4)$$

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

$$x\log(e)=\log(8.4)$$

Divide both sides by \log(e).

$$x=\frac{\log(8.4)}{\log(e)}$$

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

$$x=\log_{e}\left(8.4\right)$$

Solve for x (complex solution)

$$x=\ln(8.4)+i\times 2\pi n_{1}$$

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