Rearranging and factorizing we have

The zeros are  or

Solution set is

Factorizing we have
The zeros are  or

We factorize the inequality thus
Next we find the zeros by putting

Hence we have  or

The solution set is 

If  then

Hence 

Applying change of base we have

Applying the laws of logarithms we have .

The LHS and RHS are logarithms to the same base; hence we compare the functions thus

We divide through by y in order to get an equation in terms of what we need.
Let
 or
Hence  or

We factorize directly in terms of natural logarithms thus
 or

………(1)

……….(2  )

Using equation (1) we change  to base 2 and simplifying the equation we have

Changing from logarithmic to index form we have

……..(3)

From equation (2)
Changing from logarithmic form to index form we have
 …….(4)
Substituting (4) in (3) we have

Factoring out 2 from the bracket we have

Multiplying through by y and dividing through by  we have

Factorizing the quadratic and solving we have

We can prove this by applying logarithms thus

Using the laws of logarithms we have

Grouping like terms we have

a)
Changing to base 2 we have
Rearranging the equation we have
Factorizing directly in logarithmic form we have
Solving we have
or
b]
changing to base 3 and simplifying

Factorizing and solving we have
Hence

or