Solve 4^x*8=50

$$4 ^ { x } \times 8 = 50$$

Solve for x

$$x=\log_{2}\left(5\right)-1\approx 1.321928095$$

Steps Using Definition of Logarithm

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

$$8\times 4^{x}=50$$

Divide both sides by 8.

$$4^{x}=\frac{25}{4}$$

Take the logarithm of both sides of the equation.

$$\log(4^{x})=\log(\frac{25}{4})$$

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

$$x\log(4)=\log(\frac{25}{4})$$

Divide both sides by \log(4).

$$x=\frac{\log(\frac{25}{4})}{\log(4)}$$

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

$$x=\log_{4}\left(\frac{25}{4}\right)$$

Solve for x (complex solution)

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

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