Solve 3^x-4=27

$$3 ^ { x - 4 } = 27$$

Solve for x

$$x=7$$

Steps Using Definition of Logarithm

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

$$3^{x-4}=27$$

Take the logarithm of both sides of the equation.

$$\log(3^{x-4})=\log(27)$$

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

$$\left(x-4\right)\log(3)=\log(27)$$

Divide both sides by \log(3).

$$x-4=\frac{\log(27)}{\log(3)}$$

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

$$x-4=\log_{3}\left(27\right)$$

Add 4 to both sides of the equation.

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

Solve for x (complex solution)

$$x=\frac{i\times 2\pi n_{1}}{\ln(3)}+7$$

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