Solve 3(6)^2x-3=648

$$3 ( 6 ) ^ { 2 x - 3 } = 648$$

Solve for x

$$x=3$$

Steps Using Definition of Logarithm

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

$$3\times 6^{2x-3}=648$$

Divide both sides by 3.

$$6^{2x-3}=216$$

Take the logarithm of both sides of the equation.

$$\log(6^{2x-3})=\log(216)$$

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

$$\left(2x-3\right)\log(6)=\log(216)$$

Divide both sides by \log(6).

$$2x-3=\frac{\log(216)}{\log(6)}$$

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

$$2x-3=\log_{6}\left(216\right)$$

Add 3 to both sides of the equation.

$$2x=3-\left(-3\right)$$

Divide both sides by 2.

$$x=\frac{6}{2}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{\ln(6)}+3$$

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