SOLUTION: 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

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

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
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

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