Answer :
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]
[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]
