Answer :
To convert from exponential form to logarithmic form, we can use the following rule:
If [tex]\( a^b = c \)[/tex], then the logarithmic form is [tex]\( \log_a(c) = b \)[/tex].
In the given situation, the exponential expression is [tex]\( 9^2 = 81 \)[/tex]. Let's identify each part:
- The base [tex]\( a \)[/tex] is 9.
- The exponent [tex]\( b \)[/tex] is 2.
- The result [tex]\( c \)[/tex] is 81.
By applying the rule, we convert this into logarithmic form as follows:
[tex]\[ \log_9(81) = 2 \][/tex]
Therefore, the correct answer is D: [tex]\(\log_9(81) = 2\)[/tex].
If [tex]\( a^b = c \)[/tex], then the logarithmic form is [tex]\( \log_a(c) = b \)[/tex].
In the given situation, the exponential expression is [tex]\( 9^2 = 81 \)[/tex]. Let's identify each part:
- The base [tex]\( a \)[/tex] is 9.
- The exponent [tex]\( b \)[/tex] is 2.
- The result [tex]\( c \)[/tex] is 81.
By applying the rule, we convert this into logarithmic form as follows:
[tex]\[ \log_9(81) = 2 \][/tex]
Therefore, the correct answer is D: [tex]\(\log_9(81) = 2\)[/tex].