Solve 2*5^x/4=250

$$2 \cdot 5 ^ { x / 4 } = 250$$

Solve for x

$$x=12$$

Steps Using Definition of Logarithm

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

$$2\times 5^{\frac{1}{4}x}=250$$

Divide both sides by 2.

$$5^{\frac{1}{4}x}=125$$

Take the logarithm of both sides of the equation.

$$\log(5^{\frac{1}{4}x})=\log(125)$$

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

$$\frac{1}{4}x\log(5)=\log(125)$$

Divide both sides by \log(5).

$$\frac{1}{4}x=\frac{\log(125)}{\log(5)}$$

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

$$\frac{1}{4}x=\log_{5}\left(125\right)$$

Multiply both sides by 4.

$$x=\frac{3}{\frac{1}{4}}$$

Solve for x (complex solution)

$$x=\frac{8\pi n_{1}i}{\ln(5)}+12$$

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