# What is the answer for question 7) ? http://postimg.org/image/xusvq33e3/

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To do this we need to know the following rules.

`log_a(b) = 1/(log_b(a))` ---(1)

`log_a(b^n) = nlog_a(b)` ----(2)

Now moving to our question we can say;

`3/(log_2(a)) = 3log_a2`

`2/(log_4(a)) = 2log_a4= 2log_a(2^2) = 4log_a(2)`

`3/(log_2(a))-2/(log_4(a))`

`= 3log_a2-4log_a(2)`

`= -log_a(2)`

`= log_a(2^(-1))`   from (2)

`= log_a(1/2)`

`= 1/(log_(1/2)(a))`   from (1)

So the statement is true.

`3/(log_2(a))-2/(log_4(a)) = 1/(log_(1/2)(a))`

Sources:
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