Solve 5^2x+125=125

$${ 5 }^{ 2x+1 } 25 = 125$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

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

$$25\times 5^{2x+1}=125$$

Divide both sides by 25.

$$5^{2x+1}=5$$

Take the logarithm of both sides of the equation.

$$\log(5^{2x+1})=\log(5)$$

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

$$\left(2x+1\right)\log(5)=\log(5)$$

Divide both sides by \log(5).

$$2x+1=\frac{\log(5)}{\log(5)}$$

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

$$2x+1=\log_{5}\left(5\right)$$

Subtract 1 from both sides of the equation.

$$2x=1-1$$

Divide both sides by 2.

$$x=\frac{0}{2}$$

Solve for x (complex solution)

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

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