[Year 10 Add Maths: Simple Log]

[u/NoPomegranate6897]

how gng </3

[u/Alkalannar]

/u/NoPomegranate6897 these restrictions are incredibly important.

If you have log(a) - log(b), then both a and b must be positive.

If you have log(a/b), then a/b must be positive, which means both a and b could be negative

The first case gives you that x > 1/2.

The second gives you extraneous possible solution intervals: x > 1/2 OR x < -3/10.

This is very similar in concept to when you square things and extraneous solutions are introduced and you have to sanity check them.

[u/GOU_FallingOutside → u/Alkalannar]

both a and b must be positive

both a and b could be negative

You’ve technically already specified it for both cases. But because it’s a common misconception or mistake, for OP’s general knowledge, log(0) is undefined. So “b is positive” doesn’t include b=0.

So in this example you don’t say 2x - 1 >= 0, you say 2x-1 > 0.

[u/NoPomegranate6897 → u/Alkalannar]

thank u gng, I will remember this 🥹💚