To solve the equation [tex]\(\log_x 9 = 2\)[/tex], we need to find the value of [tex]\(x\)[/tex].
Step 1: Understand the logarithmic equation.
The given equation is [tex]\(\log_x 9 = 2\)[/tex]. This means the logarithm of 9 with base [tex]\(x\)[/tex] is 2.
Step 2: Rewriting the logarithmic equation in its exponential form.
The logarithmic equation [tex]\(\log_x 9 = 2\)[/tex] can be rewritten as an exponential equation. The general form of a logarithmic equation [tex]\(\log_b a = c\)[/tex] is equivalent to [tex]\(b^c = a\)[/tex]. Therefore:
[tex]\[ x^2 = 9 \][/tex]
Step 3: Solve the exponential equation for [tex]\(x\)[/tex].
We need to solve for [tex]\(x\)[/tex] in the equation [tex]\(x^2 = 9\)[/tex]. To do this, we take the square root of both sides of the equation:
[tex]\[ x = \sqrt{9} \][/tex]
Step 4: Calculate the value.
We know that [tex]\(\sqrt{9}\)[/tex] is 3. So:
[tex]\[ x = 3 \][/tex]
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(\boxed{3}\)[/tex].
