Solve e^4x-8=16

$$e ^ { 4 x - 8 } = 16$$

Solve for x

$$x=\ln(2)+2\approx 2.693147181$$

Steps Using Definition of Logarithm

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

$$e^{4x-8}=16$$

Take the logarithm of both sides of the equation.

$$\log(e^{4x-8})=\log(16)$$

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

$$\left(4x-8\right)\log(e)=\log(16)$$

Divide both sides by \log(e).

$$4x-8=\frac{\log(16)}{\log(e)}$$

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

$$4x-8=\log_{e}\left(16\right)$$

Add 8 to both sides of the equation.

$$4x=4\ln(2)-\left(-8\right)$$

Divide both sides by 4.

$$x=\frac{4\ln(2)+8}{4}$$