Solve (5-1/5)*5^x=24

$$( 5 - \frac { 1 } { 5 } ) \times 5 ^ { x } = 24$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$\frac{24}{5}\times 5^{x}=24$$

Divide both sides of the equation by \frac{24}{5}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$5^{x}=5$$

Take the logarithm of both sides of the equation.

$$\log(5^{x})=\log(5)$$

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

$$x\log(5)=\log(5)$$

Divide both sides by \log(5).

$$x=\frac{\log(5)}{\log(5)}$$

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

$$x=\log_{5}\left(5\right)$$

Solve for x (complex solution)

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

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