Question

solve for x.
\log_{5}x = -3
simplify your answer as much as possible.
x = \boxed{}

Explanation:

Step1: Recall the definition of logarithms

The logarithmic equation $\log_{b}a = c$ is equivalent to the exponential equation $b^{c}=a$. Here, $b = 5$, $c=- 3$, and $a = x$.

Step2: Convert the logarithmic equation to exponential form

Using the definition, we have $x = 5^{-3}$.

Step3: Simplify the exponential expression

Recall that $a^{-n}=\frac{1}{a^{n}}$, so $5^{-3}=\frac{1}{5^{3}}$. And $5^{3}=5\times5\times5 = 125$. So $x=\frac{1}{125}$.

Answer:

$\frac{1}{125}$