Yawn … yet another easy math question to solve!
Someone posted another simple math question to solve
2^x= x³²
There are two solutions, one near x = 1 and another clearly at x = 256 (this second solution is self evident). To solve for the solution near 1 take the natural logarithm
x ln 2 = 32 ln x
set the equation as
(ln x / x ) = (ln 2)/ 32
then expand the natural logarithm as
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(ln x ) / x = (2 [(x — 1 )/ (x+1)]) / x = (ln 2)/ 32
which yields you a quadratic equation, which is easily solved, providing you the first solution in an approximation of x = 1.02239 (see below). There is also the iteration approach, but that requires more effort.
Can you see how x = 256 is self evident? I will give you a clue
(ln 256)/ ln 2 = 8
and 8 x 32 = 256.
A mathematician appreciates that there may be more than one approach to a solution to a question … as simple as this one.
As a mathematician you try to solve an easy question as easily as possible, so as not to waste too much of your valuable time on trivialities.
I solved this question before my first cup of coffee this morning.
