High School

Rewrite each expression in exponential form.

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

Choose the correct option:

A. [tex]13^2 = 169[/tex]

B. [tex]169^{13} = 2[/tex]

C. [tex]2^{169} = 13[/tex]

D. [tex]2^{13} = 169[/tex]

Answer :

We are given the logarithmic equation
[tex]$$\log_{13} 169 = 2.$$[/tex]
By the definition of logarithms, this equation means that the base raised to the given exponent equals the number inside the logarithm. In general, if
[tex]$$\log_b a = c,$$[/tex]
then it is equivalent to
[tex]$$b^c = a.$$[/tex]

In our problem, by comparing we have:
- [tex]$b = 13$[/tex],
- [tex]$a = 169$[/tex], and
- [tex]$c = 2$[/tex].

Thus, rewriting the logarithmic expression into its corresponding exponential form, we obtain
[tex]$$13^2 = 169.$$[/tex]

The correct exponential form is thus option (A).

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