Solve 4^2x-3div4^4=64

$$4 ^ { 2 x - 3 } \div 4 ^ { 4 } = 64$$

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

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

$$\frac{1}{256}\times 4^{2x-3}=64$$

Multiply both sides by 256.

$$4^{2x-3}=16384$$

Take the logarithm of both sides of the equation.

$$\log(4^{2x-3})=\log(16384)$$

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

$$\left(2x-3\right)\log(4)=\log(16384)$$

Divide both sides by \log(4).

$$2x-3=\frac{\log(16384)}{\log(4)}$$

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

$$2x-3=\log_{4}\left(16384\right)$$

Add 3 to both sides of the equation.

$$2x=7-\left(-3\right)$$

Divide both sides by 2.

$$x=\frac{10}{2}$$

Solve for x (complex solution)

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

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