What is the extreme f(x)=ln((4x^2)/(ln(x))) ?

The extreme f(x)=ln((4x^2)/(ln(x))) is Minimum(sqrt(e),ln(8e))

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extreme f(x)=ln((4x^2)/(ln(x)))

extreme points

f (x) = ln (\frac{4 x ^{2}}{ln ( x )})

Minimum (e, ln (8 e))

Solution steps

f^{'} (x) = \frac{2 ln ( x ) - 1}{x ln ( x )}

Find intervals:

Decreasing

: 1 < x < e,

Increasing

: e < x < \infty

Plug

x = e

into

ln (\frac{4 x ^{2}}{ln ( x )}) : ln (8 e)

Minimum (e, ln (8 e))

What is the extreme f(x)=ln((4x^2)/(ln(x))) ?
The extreme f(x)=ln((4x^2)/(ln(x))) is Minimum(sqrt(e),ln(8e))