To convert the given exponential equation [tex]\(6^2 = 36\)[/tex] into its equivalent logarithmic form, follow these steps:
1. Identify the components of the exponential equation:
- Base: The base of the exponentiation, which is [tex]\(6\)[/tex].
- Exponent: The power to which the base is raised, which is [tex]\(2\)[/tex].
- Result: The outcome of the exponentiation, which is [tex]\(36\)[/tex].
2. Recall the relationship between exponential and logarithmic forms:
- Exponential form: [tex]\(a^b = c\)[/tex]
- Logarithmic form: [tex]\(\log_a(c) = b\)[/tex]
3. Substitute the identified components into the logarithmic form:
- Base [tex]\(a\)[/tex] is [tex]\(6\)[/tex],
- Result [tex]\(c\)[/tex] is [tex]\(36\)[/tex],
- Exponent [tex]\(b\)[/tex] is [tex]\(2\)[/tex].
4. Write the equivalent logarithmic equation:
[tex]\[
\log_6(36) = 2
\][/tex]
So, the logarithmic form of the given exponential equation [tex]\(6^2 = 36\)[/tex] is [tex]\(\log_6(36) = 2\)[/tex].
