Just jumping in, without any preliminary simplification:
log 24 + log x = log 14, so log x = (log 14) / (log 24).
Note that log 24= log 4*6 = log 4 + log 6. This isn't very helpful because 6 does not show up in any of the four answer choices.
Because of this, I realilzed that you may have meant 24^x = 14, which is vastly different from 24x = 14. It's essential that you use " ^ " to indicate exponentiation.
If 24^x = 14 is correct, then taking the log of both sides produces
x log 24 = log 14, and this is equivalent to x(log 2^3*3) = log 14. Unfortunately, this doesn't match any of the 4 possible answers either (none of them contain "3").
Please, go back to the original question and ensure that you have copied it down correctly, as well as using " ^ " to indicate exponentiation, if applicable.
