Solve 3^-x=243

$$3 ^ { - x } = 243$$

Solve for x

$$x=-5$$

Steps Using Definition of Logarithm

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

$$3^{-x}=243$$

Take the logarithm of both sides of the equation.

$$\log(3^{-x})=\log(243)$$

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

$$-x\log(3)=\log(243)$$

Divide both sides by \log(3).

$$-x=\frac{\log(243)}{\log(3)}$$

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

$$-x=\log_{3}\left(243\right)$$

Divide both sides by -1.

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

Solve for x (complex solution)

$$x=-\frac{i\times 2\pi n_{1}}{\ln(3)}-5$$

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