To rewrite the logarithmic function [tex]\(\log_b 62 = a\)[/tex] in exponential form, we start by recalling the basic definition of a logarithm:
[tex]\[
\log_b x = y \implies b^y = x
\][/tex]
In the given logarithmic equation, [tex]\(\log_b 62 = a\)[/tex], we can identify [tex]\(x\)[/tex], [tex]\(y\)[/tex], and [tex]\(b\)[/tex]:
- [tex]\(x = 62\)[/tex]
- [tex]\(b\)[/tex] is the base of the logarithm
- [tex]\(a\)[/tex] is the logarithm value
Using the above definition, we can convert [tex]\(\log_b 62 = a\)[/tex] into its equivalent exponential form:
[tex]\[
b^a = 62
\][/tex]
Therefore, the correct exponential form of the given logarithmic function [tex]\(\log_b 62 = a\)[/tex] is:
[tex]\[
\boxed{b^a = 62}
\][/tex]
This corresponds to option B.
