Solve 8^x/8=8^4

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

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

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

$$\frac{1}{8}\times 8^{x}=4096$$

Multiply both sides by 8.

$$8^{x}=32768$$

Take the logarithm of both sides of the equation.

$$\log(8^{x})=\log(32768)$$

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

$$x\log(8)=\log(32768)$$

Divide both sides by \log(8).

$$x=\frac{\log(32768)}{\log(8)}$$

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

$$x=\log_{8}\left(32768\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{3\ln(2)}+5$$

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