Question

Rewrite each logarithm as a quotient of natural logarithms. Then, evaluate to the nearest hundredth.

log(11)5 log(4)40

Answer 1

`\log_(11)(5)=0.671` and
`\log_4(40)=2.661`

Explanation:

Given:
`\log_(11)5` and
`\log_(4)40`

We have to rewrite each logarithm as a quotient of natural logarithms.

Using property of logarithm,

`\log_a(b)=(\log_eb)/(\log_ea)`

Consider 1)
`\log_(11)5`

Applying property stated above,

`\log_(11)(5)=(\log_e5)/(\log_e11)`

We have
`{\log_e5}=1.609`(approx)

`{\log_e11}=2.398`(approx)

Substitute, we get,

`\log_(11)(5)=0.671`

Consider 2)
`\log_(4)40`

Applying property stated above,

`\log_4(40)=(\log_e40)/(\log_e4)`

We have
`{\log_e40}=3.689`(approx)

`{\log_e4}=1.386`(approx)

Substitute, we get,

`\log_4(40)=2.661`

Thus,
`\log_(11)(5)=0.671` and
`\log_4(40)=2.661`