Question #eaf3e

1 Answer
Ahmet C
Oct 25, 2017

#x=2/3#

Explanation:

I'm assuming the question was

#log((x+1)/x)+log(2)=log(5)#

Some rules for logarithms:

  1. #log(A)+log(B) = log(A*B)#
  2. #log(A)-log(B) = log(A/B)#

We can use the first rule, so

#log((x+1)/x)+log(2)#

becomes

#log(2*(x+1)/x)#

Thus

#log(2*(x+1)/x) = log(5)#

Eliminate logs

#10^log(2*(x+1)/x)=10^log(5)#

#2*(x+1)/x=5#

#2x+2=5x#

#2=3x#

#x=2/3#

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