Solve 25^3k=629

$$25 ^ { 3 k } = 629$$

Solve for k

$$k=\frac{\log_{5}\left(629\right)}{6}\approx 0.667327312$$

Steps Using Definition of Logarithm

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

$$25^{3k}=629$$

Take the logarithm of both sides of the equation.

$$\log(25^{3k})=\log(629)$$

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

$$3k\log(25)=\log(629)$$

Divide both sides by \log(25).

$$3k=\frac{\log(629)}{\log(25)}$$

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

$$3k=\log_{25}\left(629\right)$$

Divide both sides by 3.

$$k=\frac{\log_{5}\left(629\right)}{2\times 3}$$