Question 16602
solve log base 2 of quantity x + 1 minus log base 4 of x equals 1

log2 of (x+1) minus log4 of x  =  1
FORMULAE...there are different bases for logs in this problem.so the main formula to be used here is that for conversion into one common base ..it is 
 log base a of quantity x OR more correctly log of x to base a = log(x)/log(a) where the base of log is any common base usually taken as base 10 ...using this we get 
 log(x+1)/log 2 - log(x)/log 4 = 1...now log 4 = log(2^2)=2log 2..hence
log(x+1)/log 2 - log(x)/2log 2 = 1
[2log(x+1)-log(x)]/2log2 =1
 [log{(x+1)^2}-log(x)] = 2log2 =log 2^2 =log 4..using lo(x)-log(y)+log(x/y)..we get
log[{(x+1)^2}/x]= log 4
  (x+1)^2/x = 4
  (x+1)^2 = 4x
 x^2+1+2x-4x = 0
 x^2+1-2x = 0
 (x-1)^2 =0
x=1