Solve 3^-2x+5=27

$$3 ^ { - 2 x + 5 } = 27$$

Solve for x

$$x=1$$

Steps Using Definition of Logarithm

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

$$3^{-2x+5}=27$$

Take the logarithm of both sides of the equation.

$$\log(3^{-2x+5})=\log(27)$$

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

$$\left(-2x+5\right)\log(3)=\log(27)$$

Divide both sides by \log(3).

$$-2x+5=\frac{\log(27)}{\log(3)}$$

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

$$-2x+5=\log_{3}\left(27\right)$$

Subtract 5 from both sides of the equation.

$$-2x=3-5$$

Divide both sides by -2.

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

Solve for x (complex solution)

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

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