Solve e^x=53

$$e ^ { x } = 53$$

Solve for x

$$x=\ln(53)\approx 3.970291914$$

Steps Using Definition of Logarithm

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

$$e^{x}=53$$

Take the logarithm of both sides of the equation.

$$\log(e^{x})=\log(53)$$

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

$$x\log(e)=\log(53)$$

Divide both sides by \log(e).

$$x=\frac{\log(53)}{\log(e)}$$

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

$$x=\log_{e}\left(53\right)$$

Solve for x (complex solution)

$$x=\ln(53)+2\pi n_{1}i$$

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