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Which logarithmic equation is equivalent to the exponential equation below?

E^a=38.47

AIn a=38.47
BLog a 38.47=3.65
CIn 38.47= a
DLog38.47 3.65=e

Verified Answer :

C is the correct answer

Answer:

C)  a =  ln (38.47).

Step-by-step explanation:

Given : \(E^{a}\) = 38.47

To find : Which logarithmic equation is equivalent to the exponential equation.

Solution : We have given that : \(E^{a}\) = 38.47.

Taking natural logarithm both sides

\(log_{e}(E^{a})\) = log(38.47).

By the  logarithm rule: \(log_{a}(a^{n})= n\) ; \(log_{e}(e) = 1.\)=1.

Then , a =  ln (38.47).

Therefore,C)  a =  ln (38.47).