Solve 5^x-4=1/5

$$5 ^ { x - 4 } = \frac { 1 } { 5 }$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$5^{x-4}=\frac{1}{5}$$

Take the logarithm of both sides of the equation.

$$\log(5^{x-4})=\log(\frac{1}{5})$$

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

$$\left(x-4\right)\log(5)=\log(\frac{1}{5})$$

Divide both sides by \log(5).

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

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

$$x-4=\log_{5}\left(\frac{1}{5}\right)$$

Add 4 to both sides of the equation.

$$x=-1-\left(-4\right)$$

Solve for x (complex solution)

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

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