Changing the base and simplifying we have.

Let 
Factorizing and solving we have
 or

But
Hence
or
But from the question  or  and  are unequal
Hence  is the right relation.

In this problem we change the base of the logarithm thus

Multiplying through by  and rearranging we have

Let
Factorising we and solving we have

 or
But
If
If

a)

To solve this question we may proceed thus Let
Then

 mog
This problem could also be solved by changing base 4 to base 2 thus:
Surely you can show that  )
b)

We can solve this problem by changing the logarithm  to base 7 or  to base 5

Multiplying through by  we have  or

Factorizing and solving we have
 or
If  and
If

Multiplying through by  we have

Reordering the equation we have

Factorizing we have

Solving we have
 or .
If
If  or

We can rewrite the equation as

Let  then the equation becomes

So
Hence  or
But , therefore  or
If  then  or  (recall the laws of logaritims)
if  then  is undefined.

Multiply through by  we have

Reordering the equation we have

Factorizing we have

Solving we have  or
If  then
If  then  or

Multiplying through by , we have
So
Factorizing we have
Solving we have  of
If
sine
 hn sha inle
1e

Let .
Factorizing we have

So  or

Also  or  is not real

.
We can express the given equation thus.
 
Now let
Factorizing we have
Hence  or
,
If
If  then  i.e.  is undefined