Answer :
To convert an equation from exponential form to logarithmic form, we follow a specific method. Let's look at the equation [tex]\(9^2 = 81\)[/tex].
1. Identify the parts of the exponential equation:
- The base is [tex]\(9\)[/tex].
- The exponent (or power) is [tex]\(2\)[/tex].
- The result is [tex]\(81\)[/tex].
2. Convert to logarithmic form:
In general, the exponential equation [tex]\( b^e = r \)[/tex] can be rewritten in logarithmic form as [tex]\( \log_b(r) = e \)[/tex].
3. Apply this to your equation:
Here, the base [tex]\(b\)[/tex] is [tex]\(9\)[/tex], the exponent [tex]\(e\)[/tex] is [tex]\(2\)[/tex], and the result [tex]\(r\)[/tex] is [tex]\(81\)[/tex].
So, the logarithmic form of [tex]\(9^2 = 81\)[/tex] is:
[tex]\[
\log_9(81) = 2
\][/tex]
Therefore, the correct answer is option D: [tex]\(\log_9(81) = 2\)[/tex].
1. Identify the parts of the exponential equation:
- The base is [tex]\(9\)[/tex].
- The exponent (or power) is [tex]\(2\)[/tex].
- The result is [tex]\(81\)[/tex].
2. Convert to logarithmic form:
In general, the exponential equation [tex]\( b^e = r \)[/tex] can be rewritten in logarithmic form as [tex]\( \log_b(r) = e \)[/tex].
3. Apply this to your equation:
Here, the base [tex]\(b\)[/tex] is [tex]\(9\)[/tex], the exponent [tex]\(e\)[/tex] is [tex]\(2\)[/tex], and the result [tex]\(r\)[/tex] is [tex]\(81\)[/tex].
So, the logarithmic form of [tex]\(9^2 = 81\)[/tex] is:
[tex]\[
\log_9(81) = 2
\][/tex]
Therefore, the correct answer is option D: [tex]\(\log_9(81) = 2\)[/tex].
