How do you simplify #log(x^2) - log(x)#?

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Answer 1 · 2016-03-27T06:11:07

#log(x^2) - log(x) = log(x)#

There is an identity

#log(ab) = log(a) + log(b)#

which is applicable.

#log(x^2)# can be written as

#log(x^2) = log(x * x)#

#= log(x) + log(x)#

#= 2log(x)#

Thus, we can write

#log(x^2) - log(x) = 2log(x) - log(x)#

#= log(x)#

Answer 2 · 2016-03-27T06:11:51

#log (x^2)-log (x)=log ((x^2)/ (x))=log x#

From Laws of logarithms

#Log (M/N)=log M- log N#

#log (x^2)-log (x)=log ((x^2)/ (x))=log x#

God bless...I hope the explanation is useful.