Question

Please help logarithms!

Answer 1

Given:

`\log_34\approx 1.262`

`\log_37\approx 1.771`

To find:

The value of
`\log_3\left((4)/(49)\right)`.

Solution:

We have,

`\log_34\approx 1.262`

`\log_37\approx 1.771`

Using properties of log, we get

`\log_3\left((4)/(49)\right)=\log_34-\log_349`
`\left[\because \log_a(m)/(n)=\log_am-\log_an\right]`

`\log_3\left((4)/(49)\right)=\log_34-\log_37^2`

`\log_3\left((4)/(49)\right)=\log_34-2\log_37`
`[\log x^n=n\log x]`

Substitute
`\log_34\approx 1.262` and
`\log_37\approx 1.771`.

`\log_3\left((4)/(49)\right)=1.262-2(1.771)`

`\log_3\left((4)/(49)\right)=1.262-3.542`

`\log_3\left((4)/(49)\right)=-2.28`

Therefore, the value of
`\log_3\left((4)/(49)\right)` is
`-2.28`.