How do you find b? In:
-1/5 loga 3^-3 + 1/4 loga 3^1/4 = 53/320
I have gotten as far as working out:
loga 193/100 + loga 11/10 = 53/320 (at least I think I have done this part correctly)
but I am unsure where to go from here. I think its something to do with y = loga(x) which is a^y = x but I'm unsure how to take it forward other than trial and error.
Should that not be:
log(x1 * x2) = logx1 + logx2 as the negatives cancel each other out (or does the - not go to the power with the 3?) and 1/16 rather than 1/8? (appologies if I have missed something).
Anyway doing it that way I got:
1822/100 is that correct?
I'm not sure now. I never wrote down my working for that part I punched it all into the calculator though I some how ended up with:
loga 2122/1000 = 53/320
so a^53/320 = 2122/1000
so a = root 53/320 of 2122/1000 (I'm not sure if thats expressed correctly).
But no matter what working I do now I cannot get 2122/1000, I must have made a mistake somewhere as doing what I though I'd done.
Also I don't understand how you are getting 1/8 rather than a 1/16, could you explain that please?
Anyway taking what you have up there I and doing what I did above I got 123.36