How to solve 125 ^ (x/3) = 25

1. Factor the equation (x + 2)(x + 3) = 0. 2. Set each factor equal to zero: x + 2 = 0 and x + 3 = 0. 3. Solve for x: x = -2 and x = -3.

Solve 125 ^ (x/3) = 25 | Equatix

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$$125^{\frac{x}{3}}=25$$

$x=2$

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

$$125^{\frac{1}{3}x}=25$$

Take the logarithm of both sides of the equation.

$$\log(125^{\frac{1}{3}x})=\log(25)$$

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

$$\frac{1}{3}x\log(125)=\log(25)$$

Divide both sides by $\log(125)$.

$$\frac{1}{3}x=\frac{\log(25)}{\log(125)}$$

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

$$\frac{1}{3}x=\log_{125}\left(25\right)$$

Multiply both sides by $3$.

$$x=\frac{\frac{2}{3}}{\frac{1}{3}}$$

$x=\frac{i\times 2\pi n_{1}}{\ln(5)}+2$
$n_{1}\in \mathrm{Z}$