text: how to do this math question? simplify the following without using a calculator: log(2(radical2) - 3log(radical3) - 3  all over log9 - log 4 + 4  the answer should be -3/4, but i just can't get that one. does anyone know how to work that out? okay, let's see if we can get through this.  i'll use "r" instead of "radical" just to keep it a bit shorter  [log(2r2) - 3log(r3) - 3] / [log 9 - log 4 + 4]  start in the top.  notice that 2r2 = 2(2^1/2) = 2^3/2 (2 to the 3/2 power).  likewise, r3 = 3^1/2 (3 to the 1/2 power).  so:  [log(2^3/2) - 3log(3^1/2) - 3] / [log 9 - log 4 + 4]  now remember that an exponent within a logarithm moves out to the front.  so:  [(3/2)(log 2) - (3/2)(log 3) - 3] / [log 9 - log 4 + 4]  now factor out the 3/2 from each of the terms:  [(3/2)(log 2 - log 3 - 2] / [log 9 - log 4 + 4]  now let's go to the denominator.  we'll rewrite the values 9 and 4 as squares, then move the exponents out like we did before.  [(3/2)(log 2 - log 3 - 2)] / [log(3^2) - log(2^2) + 4] [(3/2)(log 2 - log 3 - 2)] / [2 log 3 - 2 log 2 + 4]  now factor 2 out of each term in the denominator.  [(3/2)(log 2 - log 3 - 2)] / [2(log 3 - log 2 + 2)]  one more little thing to make this work.  we actually need the signs changed in the numerator, so let's factor out a -1 from each term (we should have factored out -3/2 earlier):  [(-3/2)(log 3 - log 2 + 2)] / [2(log 3 - log 2 + 2)]  now notice that the top and bottom both have (log 3 - log 2 + 2).  since this appears on both top and bottom, cancel it out.  this leaves us with:  (-3/2) / 2 -3/4  i know this was long and drawn out--i hope you followed the steps.