SOLUTION: log[base2](x+1)-log[base4]x=1 note: book says to change log[base4]x to base 2. ANSWER IS {1}. Can not figure how they arrived at the answer x 2 days!!! I know how to chan

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: log[base2](x+1)-log[base4]x=1 note: book says to change log[base4]x to base 2. ANSWER IS {1}. Can not figure how they arrived at the answer x 2 days!!! I know how to chan      Log On


   

Question 1119200: log[base2](x+1)-log[base4]x=1
note: book says to change log[base4]x to base 2.
ANSWER IS {1}.
Can not figure how they arrived at the answer x 2 days!!! I know how to change from base 4 to base 2.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


log[base2] of a number x is twice log[base4] of the same number x, because 4 is 2 squared:

log[base 4}x = n --> x = 4^n = (2^2)^n = 2^(2n) --> log[base2]x = 2n

Your book says to change log[base4]x to an equivalent expression involving log[base2]. Since log[base4] of a number is half of log[base2] of the same number, that would introduce fractions into the calculations.

I would much rather change the log[base2] expression into an equivalent expression using log[base4].

log%282%2C%28x%2B1%29%29-log%284%2Cx%29+=+1 given equation
2%2Alog%284%2C%28x%2B1%29%29-log%284%2Cx%29+=+1 convert log base 2 to log base 4
log%284%2C%28x%2B1%29%5E2%29-log%284%2Cx%29+=+1 n*log(x) = log(x^n)
log%284%2C%28%28%28x%2B1%29%5E2%29%2Fx%29%29+=+1 log(a)-log(b) = log(a/b)
%28%28x%2B1%29%5E2%29%2Fx+=+4%5E1+=+4 definition of logarithms
x%5E2%2B2x%2B1+=+4x
x%5E2-2x%2B1+=+0
%28x-1%29%5E2+=+0
x+=+1