To solve for [tex]\( x \)[/tex] in the equation [tex]\(\log_3 9 = x\)[/tex], let's follow these steps:
1. Understand the Definition of Logarithms:
The logarithmic equation [tex]\(\log_b a = c\)[/tex] is equivalent to the exponential equation [tex]\(b^c = a\)[/tex]. Here [tex]\(b\)[/tex] is the base, [tex]\(a\)[/tex] is the result, and [tex]\(c\)[/tex] is the exponent.
2. Rewrite the Given Equation:
Given [tex]\(\log_3 9 = x\)[/tex], we can rewrite it using the definition of logarithms:
[tex]\[
3^x = 9
\][/tex]
3. Express 9 as a Power of 3:
We know that [tex]\(9\)[/tex] can be expressed as a power of 3:
[tex]\[
9 = 3^2
\][/tex]
4. Substitute Back:
Now substitute this expression into our rewritten equation:
[tex]\[
3^x = 3^2
\][/tex]
5. Equate the Exponents:
Since the bases are the same, we can equate the exponents:
[tex]\[
x = 2
\][/tex]
Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[
x = 2
\][/tex]
So, we find that [tex]\(\boxed{2}\)[/tex] is the solution to the equation [tex]\(\log_3 9 = x\)[/tex].
