How to solve ((1)/(5))^(x)=125

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 ((1)/(5))^(x)=125 | Equatix

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

$x=-3$

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

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

Take the logarithm of both sides of the equation.

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

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

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

Divide both sides by $\log(\frac{1}{5})$.

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

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

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

$x=-\frac{2\pi n_{1}i}{\ln(5)}-3$
$n_{1}\in \mathrm{Z}$