Solve 5^3x-7=25

$$5 ^ { 3 x - 7 } = 25$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$5^{3x-7}=25$$

Take the logarithm of both sides of the equation.

$$\log(5^{3x-7})=\log(25)$$

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

$$\left(3x-7\right)\log(5)=\log(25)$$

Divide both sides by \log(5).

$$3x-7=\frac{\log(25)}{\log(5)}$$

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

$$3x-7=\log_{5}\left(25\right)$$

Add 7 to both sides of the equation.

$$3x=2-\left(-7\right)$$

Divide both sides by 3.

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

Solve for x (complex solution)

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

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