Solve (1/25)quad=5^x+5

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

Solve for x

$$x=-7$$

Steps Using Definition of Logarithm

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

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

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by \log(5).

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

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

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

Subtract 5 from both sides of the equation.

$$x=-2-5$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(5)}-7$$

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