Solve 2^4x13/16=208

$${ 2 }^{ 4x } \frac{ 13 }{ 16 } =208$$

Solve for x

$$x=2$$

Steps Using Definition of Logarithm

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

$$\frac{13}{16}\times 2^{4x}=208$$

Divide both sides of the equation by \frac{13}{16}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$2^{4x}=256$$

Take the logarithm of both sides of the equation.

$$\log(2^{4x})=\log(256)$$

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

$$4x\log(2)=\log(256)$$

Divide both sides by \log(2).

$$4x=\frac{\log(256)}{\log(2)}$$

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

$$4x=\log_{2}\left(256\right)$$

Divide both sides by 4.

$$x=\frac{8}{4}$$

Solve for x (complex solution)

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

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