Solve 18^x-5=25

$$18 ^ { x - 5 } = 25$$

Solve for x

$$x=2\log_{18}\left(5\right)+5\approx 6.113654607$$

Steps Using Definition of Logarithm

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

$$18^{x-5}=25$$

Take the logarithm of both sides of the equation.

$$\log(18^{x-5})=\log(25)$$

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

$$\left(x-5\right)\log(18)=\log(25)$$

Divide both sides by \log(18).

$$x-5=\frac{\log(25)}{\log(18)}$$

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

$$x-5=\log_{18}\left(25\right)$$

Add 5 to both sides of the equation.

$$x=2\log_{18}\left(5\right)-\left(-5\right)$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(18)}+2\log_{18}\left(5\right)+5$$

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