Daniel is using logarithms to solve the equation 24x = 14. which of the following equations would be equivalent to his original expression? 2 log 4x = log 14 4x log 2 = log 14 2 log 4 = x log 14 x log 4 = 2 log 14

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.