Question

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

log(9)12

Answer 1

`\log_912=1.131`

Explanation:

Given expression
`\log_912` ,

we have to rewrite the logarithm as a quotient of common logarithms and then evaluate

Using property of logarithm ,

`\log_a(b)=(\log_e(b))/(\log_e(a))`

Given expression

`\log_912` becomes,

`\log_9(12)=(\log_e(12))/(\log_e(9))`

`\log_e12 =2.485`(approx))

`\log_e9 =2.197`(approx)

Substitute , we get,

`(\log_e 12)/(\log_e 9) = 1.131`

Thus,
`\log_912=1.131`