Solve 3^3x-47=81

$$3 ^ { 3 x - 47 } = 81$$

Solve for x

$$x=17$$

Steps Using Definition of Logarithm

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

$$3^{3x-47}=81$$

Take the logarithm of both sides of the equation.

$$\log(3^{3x-47})=\log(81)$$

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

$$\left(3x-47\right)\log(3)=\log(81)$$

Divide both sides by \log(3).

$$3x-47=\frac{\log(81)}{\log(3)}$$

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

$$3x-47=\log_{3}\left(81\right)$$

Add 47 to both sides of the equation.

$$3x=4-\left(-47\right)$$

Divide both sides by 3.

$$x=\frac{51}{3}$$

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{3\ln(3)}+17$$

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