Solve 3^(8-2x)=81

$${ 3 }^{ (8-2x) } =81$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$3^{-2x+8}=81$$

Take the logarithm of both sides of the equation.

$$\log(3^{-2x+8})=\log(81)$$

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

$$\left(-2x+8\right)\log(3)=\log(81)$$

Divide both sides by \log(3).

$$-2x+8=\frac{\log(81)}{\log(3)}$$

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

$$-2x+8=\log_{3}\left(81\right)$$

Subtract 8 from both sides of the equation.

$$-2x=4-8$$

Divide both sides by -2.

$$x=-\frac{4}{-2}$$

Solve for x (complex solution)

$$x=-\frac{\pi n_{1}i}{\ln(3)}+2$$

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