Question

Given that log_{a}(3) = 0.477 and

log_{a}(5) = 0.699, evaluate log_{a}(0.6) .​

*The answer is -0.222 but I'm not sure how to do the steps.

Answer 1

Given:

`\log_(a)(3) = 0.477,\log_(a)(5) = 0.699`

To find:

The value of
`\log_(a)(0.6)`.

Solution:

We need to find the value of:

`\log_(a)(0.6)`

It can be written as

`\log_(a)(0.6)=\log_a\left((6)/(10)\right)`

`\log_(a)(0.6)=\log_a\left((3)/(5)\right)`

By using the property of logarithm, we get

`\log_(a)(0.6)=\log_a(3)-\log_a(5)`
`[\because \log (a)/(b)=\log a-\log b]`

`\log_(a)(0.6)=\log_a(3)-\log_a(5)`

On substituting the given values, we get

`\log_(a)(0.6)=0.477-0.699`

`\log_(a)(0.6)=-0.222`

Therefore, the values of
`\log_a(0.6)` is -0.222.