College

Convert [tex]9^2 = 81[/tex] to logarithmic form.

A. [tex]\log_9(2) = 81[/tex]
B. [tex]\log_{81}(2) = 9[/tex]
C. [tex]\log_2(9) = 81[/tex]
D. [tex]\log_9(81) = 2[/tex]
E. [tex]\log_{81}(9) = 2[/tex]
F. None of the above

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].

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