Solve 3^-4*81=3^x

$$3 ^ { - 4 } \times 81 = 3 ^ { x }$$

Solve for x

$$x=0$$

Steps Using Definition of Logarithm

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{1}{81}\times 81=3^{x}$$

Multiply \frac{1}{81} and 81 to get 1.

$$1=3^{x}$$

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

$$3^{x}=1$$

Take the logarithm of both sides of the equation.

$$\log(3^{x})=\log(1)$$

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

$$x\log(3)=\log(1)$$

Divide both sides by \log(3).

$$x=\frac{\log(1)}{\log(3)}$$

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

$$x=\log_{3}\left(1\right)$$

Solve for x (complex solution)

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

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