Solve 3*{4}^frac{x{2}}=96

$$3 \times { 4 }^{ \frac{ x }{ 2 } } =96$$

Solve for x

$$x=5$$

Steps Using Definition of Logarithm

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

$$3\times 4^{\frac{1}{2}x}=96$$

Divide both sides by 3.

$$4^{\frac{1}{2}x}=32$$

Take the logarithm of both sides of the equation.

$$\log(4^{\frac{1}{2}x})=\log(32)$$

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

$$\frac{1}{2}x\log(4)=\log(32)$$

Divide both sides by \log(4).

$$\frac{1}{2}x=\frac{\log(32)}{\log(4)}$$

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

$$\frac{1}{2}x=\log_{4}\left(32\right)$$

Multiply both sides by 2.

$$x=\frac{\frac{5}{2}}{\frac{1}{2}}$$

Solve for x (complex solution)

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

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