Question

solve for x.
\log_{7}x = -2
simplify your answer as much as possible.
x = \square

Explanation:

Step1: Recall the logarithm definition

The logarithmic equation $\log_b a = c$ is equivalent to the exponential equation $b^c = a$.
For the equation $\log_7 x = -2$, we can rewrite it using the definition of logarithms. Here, $b = 7$, $c = -2$, and $a = x$. So we have $7^{-2}=x$.

Step2: Simplify the exponential expression

We know that $a^{-n}=\frac{1}{a^n}$. So $7^{-2}=\frac{1}{7^2}$. And $7^2 = 49$, so $\frac{1}{7^2}=\frac{1}{49}$. Thus, $x=\frac{1}{49}$.

Answer:

$\frac{1}{49}$