Simplifying the equation we have

Let  then
Dividing through by 2 the common factor to the terms,

Factorizing we have
Hence  or
But , so  or
Therefore  or  i.e.  is undefined.

We rewrite the equation thus:

Let  then
Factorizing we have

 or
But
Hence  or
If , then
Also if  (  is undefined or  is notareal number)

We express the equation as

Let
Factorising we have
 or
 or
But , so  or
Considering
We apply logarithms thus


If  then,  which means no real number satishes the equation.

, then
Factorising, we have

 or
But  or   or
By comparison of powers we have  or

i)

 ii) We see that the proposition  is always true.
Hence it is a tautology.

Applying change of base we have