Question

Given that `log_7 x^2y = p` and `log_7 xy^2=q`, how do you find `log_7 root 3(xy` in terms of `p` and `q`?

Answer 1

`log_7root(3)(xy)=(p+q)/9`

Explanation:

As `log_7 x^2y = p` and `log_7 xy^2=q`

we have `p+q=log_7 x^2y+log_7 xy^2`

= `log_7(x^2yxx xy^2)`

= `log_7(x^3y^3)`

= `log_7(xy)^3`

= `3log_7(xy)`

Hence `log_7root(3)(xy)`

= `1/3log_7(xy)`

= `1/3xx((p+q)/3)`

= `(p+q)/9`