Solve 5^4x+8=1quad,c

$$5 ^ { 4 x + 8 } = 1 \quad , c$$

Solve for x

$$x=-2$$

Steps Using Definition of Logarithm

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

$$5^{4x+8}=1$$

Take the logarithm of both sides of the equation.

$$\log(5^{4x+8})=\log(1)$$

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

$$\left(4x+8\right)\log(5)=\log(1)$$

Divide both sides by \log(5).

$$4x+8=\frac{\log(1)}{\log(5)}$$

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

$$4x+8=\log_{5}\left(1\right)$$

Subtract 8 from both sides of the equation.

$$4x=-8$$

Divide both sides by 4.

$$x=-\frac{8}{4}$$