Math CentralQuandaries & Queries


CB, a student:

I am trying to solve lnx +3ln2 = ln 2/x. Every way I've tried when I go to plug in the solution it doesn't come out right.


I'm going to illustrate with a similar problem.
Solve ln(1/3 x2) + 2 ln(3) = ln(15 x)
I need to use two of the properties of logs which are

a ln(b) = ln(ba) and ln(a * b) = ln(a) + ln(b)

Thus 2 ln(3) = ln(32) = ln(9) and hence

ln(1/3 x2) + 2 ln(3) = ln(1/3 x2) + ln(9) = ln(1/3 * 9 x2) = ln(3 x2)

Hence ln(1/3 x2) + 2 ln(3) = ln(15 x) becomes

ln(3 x2) = ln(15 x) or 3x2 = 15x


3x2 - 15x = 0
3x(x-5) = 0

Hence x = 0 or x = 5.

But ln(0) is undefined so the only solution is x = 5.

I hope this helps,

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