Friday, October 31, 2014

3 ln x - ln 3 = 3

First, we'll impose the constraint of existence of
logarithms:


x>0


Now,
we'll use the power property of logarithms, so that:


3 ln x
= ln x^3


We'll re-write the
equation:


 ln x^3  - ln 3 =
3


Since the bases of logarithms are matching, we'll use the
quotient rule:


ln (x^3/3) =
3


We'll have:


x^3/3 =
e^3


x^3 = 3e^3


x
= e*[(3)^1/3
]


Since the
solution is positive, it is valid.

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