Solve 25+125/6=5^x+1

$$\frac { 25 + 125 } { 6 } = 5 ^ { x + 1 }$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

Multiply both sides of the equation by 6.

$$25+125=6\times 5^{x+1}$$

Add 25 and 125 to get 150.

$$150=6\times 5^{x+1}$$

Swap sides so that all variable terms are on the left hand side.

$$6\times 5^{x+1}=150$$

Divide both sides by 6.

$$5^{x+1}=\frac{150}{6}$$

Divide 150 by 6 to get 25.

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

Take the logarithm of both sides of the equation.

$$\log(5^{x+1})=\log(25)$$

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

$$\left(x+1\right)\log(5)=\log(25)$$

Divide both sides by \log(5).

$$x+1=\frac{\log(25)}{\log(5)}$$

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

$$x+1=\log_{5}\left(25\right)$$

Subtract 1 from both sides of the equation.

$$x=2-1$$

Solve for x (complex solution)

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

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