Solve 5^4x=600

$$5 ^ { 4 x } = 600$$

Solve for x

$$x=\frac{\log_{5}\left(600\right)}{4}\approx 0.993658967$$

Steps Using Definition of Logarithm

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

$$5^{4x}=600$$

Take the logarithm of both sides of the equation.

$$\log(5^{4x})=\log(600)$$

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

$$4x\log(5)=\log(600)$$

Divide both sides by \log(5).

$$4x=\frac{\log(600)}{\log(5)}$$

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

$$4x=\log_{5}\left(600\right)$$

Divide both sides by 4.

$$x=\frac{\log_{5}\left(600\right)}{4}$$