Solve 5^9-x=625

$$5 ^ { 9 - x } = 625$$

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

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

$$5^{-x+9}=625$$

Take the logarithm of both sides of the equation.

$$\log(5^{-x+9})=\log(625)$$

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

$$\left(-x+9\right)\log(5)=\log(625)$$

Divide both sides by \log(5).

$$-x+9=\frac{\log(625)}{\log(5)}$$

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

$$-x+9=\log_{5}\left(625\right)$$

Subtract 9 from both sides of the equation.

$$-x=4-9$$

Divide both sides by -1.

$$x=-\frac{5}{-1}$$

Solve for x (complex solution)

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

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