SOLUTION: Bob incorrectly reasons that logb 1/x= logb x/xx Bob's answer- =logb x-logb x+logb x=logb x. What mistake has Bob made?

Question 1030384: Bob incorrectly reasons that logb 1/x= logb x/xx
Bob's answer- =logb x-logb x+logb x=logb x.
What mistake has Bob made?
Answer by JoelSchwartz(130) (Show Source): You can put this solution on YOUR website!
log b (x) - log b (x) + log b (x) = log b (x)
x/x + log b (x) = log b (x)
1 = log b (x) - log b (x)
Bob has not solved that log b (1/x) = log b (x/x^2)
he has only solved x/x equals one
to solve this equation here is the work required
log b (1) - log b (x) = log b (x) - log b (x^2)
log b (1) = log b (x) + log b (x) - log b (x^2)
log b (1) = log b (x^2) - log b (x^2)
(x^2)/(x^2)=1
x^2=x^2

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