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------------------------------------------------ What is the logarithmic form of [tex]13^2=169[/tex]?

A. [tex]\log_{13} 2 = 169[/tex]
B. [tex]\log_{2} 13 = 169[/tex]
C. [tex]\log_{2} 169 = 13[/tex]
D. [tex]\log_{13} 169 = 2[/tex]

To convert the equation [tex]\(13^2 = 169\)[/tex] into its logarithmic form, we need to follow the general understanding of logarithms. The logarithmic form of an equation [tex]\(a^b = c\)[/tex] is expressed as:

[tex]\[
\log_a(c) = b
\][/tex]

In this case, using the equation [tex]\(13^2 = 169\)[/tex]:

- The base [tex]\(a\)[/tex] is 13.
- The exponent [tex]\(b\)[/tex] is 2.
- The result [tex]\(c\)[/tex] is 169.

By substituting these values into the logarithmic form, we have:

[tex]\[
\log_{13}(169) = 2
\][/tex]

Thus, the correct logarithmic form of the equation [tex]\(13^2 = 169\)[/tex] is [tex]\(\log_{13}(169) = 2\)[/tex]. So, the answer is:

[tex]\[
\log_{13} 169 = 2
\][/tex]