Explanation:
whoever created the original question and then probably the people copying it need to focus on writing these things correctly.
I assume this means
log(9) - log(4) ÷ log(3) - log(2)
or is anything combined in brackets ? like it could be e.g. log(4 ÷ log(3)). just as example.
and I guess we mean logarithm to the base of 10, right ?
anyway, if my assumptions are correct, then we only need to follow the regular priorities of mathematical operations :
1. brackets
2. exponents
3. multiplications and divisions
4. additions and subtractions
so, we need to start with the division in the middle, and then do the subtractions.
log(4) ÷ log(3) = 1.261859507...
log(9) - 1.261859507... = -0.307616998...
-0.307616998... - log(2) = -0.608646993...
or was the original question
(log(9) - log(4)) ÷ (log(3) - log(2))
?
that would be way more interesting.
we use the rules of logarithm :
e.g.
log(a×b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
so, we have then
log(9/4) ÷ log(3/2)
and that is equal to
log(3/2 × 3/2) ÷ log(3/2)
(log(3/2) + log(3/2)) ÷ log(3/2) = 1 + 1 = 2
if that is the case, you really, REALLY need to pay more attention to brackets and other symbols in problem definitions.