Solve 10^x-3=25

$$10 ^ { x - 3 } = 25$$

Solve for x

$$x=\log_{10}\left(25000\right)\approx 4.397940009$$

Steps Using Definition of Logarithm

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

$$10^{x-3}=25$$

Take the logarithm of both sides of the equation.

$$\log(10^{x-3})=\log(25)$$

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

$$\left(x-3\right)\log(10)=\log(25)$$

Add 3 to both sides of the equation.

$$x=2\log(5)-\left(-3\right)$$

Solve for x (complex solution)

$$x=\frac{2\pi n_{1}i}{\ln(10)}+\log_{10}\left(25000\right)$$

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