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 Post subject: what happens when you square a natural log?Posted: Thu, 17 May 2012 13:30:50 UTC
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Joined: Thu, 15 Dec 2011 16:54:36 UTC
Posts: 16
All,

what is (ln(x))^2 equal to?

is it something like 2ln(x)? or possibly ln(2x)? or possibly ln(x^2)?

or are we simply stuck at (ln(x))^2?

Jeff

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 Post subject: Re: what happens when you square a natural log?Posted: Thu, 17 May 2012 14:38:20 UTC

Joined: Sat, 26 Apr 2003 22:14:40 UTC
Posts: 2063
Location: El Paso TX (USA)
As you say: we are stuck at .

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 Post subject: Re: what happens when you square a natural log?Posted: Thu, 17 May 2012 16:56:17 UTC
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Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 3692
Location: Ottawa Ontario
In other words: 2^x = x + 5
cannot be directly solved...even if "apparently obvious" that x=3.

x = log(x + 5) / log(2)
or
2 = (x + 5)^(1/x)

This is all similar to financial formulas where i (periodic interest rate)
has to be calculated involving periodic payments; as example,
FV = P[(1 + i)^N] / i : Future Value of \$P per period for N periods
If FV, P and N are given, then i had to be determined numerically.

Jeff, thanks for reminding me that exp(x) = e^x.

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