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
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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) (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].
given equation
convert log base 2 to log base 4
n*log(x) = log(x^n)
log(a)-log(b) = log(a/b)
definition of logarithms
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