Solve 25^x+1=1

$$25 ^ { x + 1 } = 1$$

Solve for x

$$x=-1$$

Steps Using Definition of Logarithm

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

$$25^{x+1}=1$$

Take the logarithm of both sides of the equation.

$$\log(25^{x+1})=\log(1)$$

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

$$\left(x+1\right)\log(25)=\log(1)$$

Divide both sides by \log(25).

$$x+1=\frac{\log(1)}{\log(25)}$$

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

$$x+1=\log_{25}\left(1\right)$$

Subtract 1 from both sides of the equation.

$$x=-1$$

Solve for x (complex solution)

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

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