Answer :
To express the equation [tex]\(169 = 13^2\)[/tex] in logarithmic form, we need to rewrite it using the definition of a logarithm.
In general, the logarithmic form of an equation of the type [tex]\(a^b = c\)[/tex] is expressed as [tex]\(\log_a(c) = b\)[/tex]. Here's how it applies to the given equation:
1. Identify the components:
- The base [tex]\(a\)[/tex] of the exponentiation is 13.
- The exponent [tex]\(b\)[/tex] is 2.
- The result [tex]\(c\)[/tex] of the exponentiation is 169.
2. Rewrite the equation [tex]\(169 = 13^2\)[/tex] in logarithmic form:
- According to the definition, convert the expression to [tex]\(\log_{13}(169) = 2\)[/tex].
This logarithmic expression indicates that 13 raised to the power of 2 equals 169.
In general, the logarithmic form of an equation of the type [tex]\(a^b = c\)[/tex] is expressed as [tex]\(\log_a(c) = b\)[/tex]. Here's how it applies to the given equation:
1. Identify the components:
- The base [tex]\(a\)[/tex] of the exponentiation is 13.
- The exponent [tex]\(b\)[/tex] is 2.
- The result [tex]\(c\)[/tex] of the exponentiation is 169.
2. Rewrite the equation [tex]\(169 = 13^2\)[/tex] in logarithmic form:
- According to the definition, convert the expression to [tex]\(\log_{13}(169) = 2\)[/tex].
This logarithmic expression indicates that 13 raised to the power of 2 equals 169.
