How to solve 5 ^ x = 1/25

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 5 ^ x = 1/25 | Equatix

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$$5 ^ { x } = \frac { 1 } { 25 }$$

$x=-2$

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

$$5^{x}=\frac{1}{25}$$

Take the logarithm of both sides of the equation.

$$\log(5^{x})=\log(\frac{1}{25})$$

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

$$x\log(5)=\log(\frac{1}{25})$$

Divide both sides by $\log(5)$.

$$x=\frac{\log(\frac{1}{25})}{\log(5)}$$

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

$$x=\log_{5}\left(\frac{1}{25}\right)$$

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