Solve 5*2^8x=15

$$5 \times { 2 }^{ 8x } =15$$

Solve for x

$$x=\frac{\log_{2}\left(3\right)}{8}\approx 0.198120313$$

Steps Using Definition of Logarithm

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

$$5\times 2^{8x}=15$$

Divide both sides by 5.

$$2^{8x}=3$$

Take the logarithm of both sides of the equation.

$$\log(2^{8x})=\log(3)$$

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

$$8x\log(2)=\log(3)$$

Divide both sides by \log(2).

$$8x=\frac{\log(3)}{\log(2)}$$

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

$$8x=\log_{2}\left(3\right)$$

Divide both sides by 8.

$$x=\frac{\log_{2}\left(3\right)}{8}$$

Solve for x (complex solution)

$$x=\frac{\pi n_{1}i}{4\ln(2)}+\frac{\log_{2}\left(3\right)}{8}$$

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