Question

Whenever w is an integer greater than 1, logw w^2/w^6=?

-4
-3
-1/3
1/3
3

Answer 1

Option (1)

Explanation:

Given expression is,

`\text{log_w((w^2)/(w^6))}`
`\text{log}_w((w^2)/(w^6) )`

Let the given expression is equal to y.

`\text{log}_w((w^2)/(w^6) )=y`

By applying logarithmic rule,

`((w^2)/(w^6) )=w^y`

`w^2* w^(-6)=w^y`

`w^(2-6)=w^y`

`w^(-4)=w^y`

`y=-4`

Therefore, value of the given expression
`\text{log}_w((w^2)/(w^6) )=-4`.

Option (1) will be the correct option.