Question

Find the values of h and k which are ?

Given that `log_2 hk` = 3 and `log_2 h^3 k^2` = 5

Answer 1

`h = 2^-1 = 1/2` and `k = 2^4 = 16`

Explanation:

`log_2hk = 3` if and only if `hk=2^3`, so `k=2^3/h`

`loh_2h^3k^2 = 5` if and only if `h^3k^2=2^5`,

Using `k=2^3/h`, we get

`h^3(2^3/h)^2=2^5` and

`(h^3 2^6)/h^2 = 2^5`

`h = 2^5/2^6 = 2^-1 = 1/2`

and `k=2^3/2^-1 = 2^4`