Hello!
Um... I ended up with
Log(16x) = log16 + logx = log(2^4) + a = 4 log2 + a = 4 + a
(because log 2 is 1 if you are using logs in base 2 – sorry, can’t get the editor to take subscripts)
And
Log (x^4/2) = log (x^4) – log 2 = 4 log x - log 2 = 4 log x – 1 = 4a – 1
Combining these gives
Log(16x) – log (x^4/2) = 4 + a – (4a – 1) = 4 + a – 4a + 1 = 5 – 3a
Now the question says that this is 1/2, so
5 – 3a = 1/2, so 3a = 9/2 (aka 4.5) and so a = 3/2
So if log x = a, and a = 3/2,
then log x = 3/2 and so x = 2^(3/2)
so x = the square root of 8 aka 2root2 (in its simplest surd form)
That any use?
love danni
PS Knogle, sorry but when you split the log(16x) into log 8 + log (2x) you'd either misread the 16x as 8x or decided the 2 in 2x was the base not the, er, thing you were taking the log of (if that makes sense)