To solve the equation [tex]\(6^x = 36\)[/tex], let's go through these steps:
1. Express 36 as a power of 6:
We know that [tex]\(36\)[/tex] can be rewritten as [tex]\(6^2\)[/tex], because:
[tex]\[
36 = 6 \times 6 = 6^2
\][/tex]
2. Substitute [tex]\(36\)[/tex] with [tex]\(6^2\)[/tex] in the equation:
The original equation is:
[tex]\[
6^x = 36
\][/tex]
By substituting [tex]\(36\)[/tex] with [tex]\(6^2\)[/tex], we get:
[tex]\[
6^x = 6^2
\][/tex]
3. Compare exponents:
Since the bases are the same (both are [tex]\(6\)[/tex]), we can set the exponents equal to each other:
[tex]\[
x = 2
\][/tex]
Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation [tex]\(6^x = 36\)[/tex] is [tex]\( \boxed{2} \)[/tex].
