Question

Which logarithmic equation is equivalent to the exponential equation below?

87.18= e^a

A. Log87.18 3.45=e
B. In 87.18=a
C. Loga 87.18=3.45
D. In a= 87.18

Answer 1

The answer is B.
ln both sides to clear the 'e' and bring 'a' out of the power.

Answer 2

B.
`\ln 87.18=a`

Explanation:

We are given,

The logarithmic equation is
`87.18=e^a`.

Taking log with base 'e' on both sides, we get,

`87.18=e^a`

i.e.
`\log_(e)87.18=\log_(e)e^a` ............(
`\log x^y=y\log x`)

i.e.
`\log_(e)87.18=a\log_(e)e` ............(
`\log_(a)a=1`

i.e.
`\log_(e)87.18=a`

Thus, option B is correct.