Solve 16^3/4=4^x

$$16 ^ { 3 / 4 } = 4 ^ { x }$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps Using Definition of Logarithm

Calculate 16 to the power of \frac{3}{4} and get 8.

$$8=4^{x}$$

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

$$4^{x}=8$$

Take the logarithm of both sides of the equation.

$$\log(4^{x})=\log(8)$$

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

$$x\log(4)=\log(8)$$

Divide both sides by \log(4).

$$x=\frac{\log(8)}{\log(4)}$$

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

$$x=\log_{4}\left(8\right)$$

Solve for x (complex solution)

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

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