Mistake from 1 of the steps onwards. You can't multiply by (y - 2) as it is not known if y - 2 is positive or negative.

It is an inequality sign and not an equals sign. You can only multiply by y - 2 if you know what y-2 's sign is. (and therefore decide whether to flip the sign or not)

Or,

when it's an equals sign.

The terms on the right hand side should be brought to the left , then factorised. Sign checking is done afterwards.

You may refer to my working on the main comments section.

Secondly, log3(x) = 4 is incorrect also.


the inequality is found to be 3 < y < 5. Replacing y with log3(x) gives :


3 < log3(x) < 5

Question gives x to be positive integer. We have to first solve this inequality before deciding which positive values of x satisfy it.


i.e


log3(3³) < log3(x) < log3(3^5)

3³ < x < 3^5

27 < x < 243


So the possible values of x are positive integers from 28 to 242, inclusive.



The other inequality that you've missed out was 0 < log3(x) < 2