Question

Which logarithmic equation is equivalent to the exponential equation below?

E^a=38.47

A. In a=38.47
B. Log a 38.47=3.65
C. In 38.47= a
D. Log38.47 3.65=e

Answer 1

C is the correct answer

Answer 2

C) a = ln (38.47).

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).