Solve 5^3x-5=625

$$5 ^ { 3 x - 5 } = 625$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$5^{3x-5}=625$$

Take the logarithm of both sides of the equation.

$$\log(5^{3x-5})=\log(625)$$

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

$$\left(3x-5\right)\log(5)=\log(625)$$

Divide both sides by \log(5).

$$3x-5=\frac{\log(625)}{\log(5)}$$

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

$$3x-5=\log_{5}\left(625\right)$$

Add 5 to both sides of the equation.

$$3x=4-\left(-5\right)$$

Divide both sides by 3.

$$x=\frac{9}{3}$$

Solve for x (complex solution)

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

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