What is the inflection (ln(x-2))/((x-2)^2) ?

The inflection (ln(x-2))/((x-2)^2) is (e^{5/6}+2, 5/(6e^{5/3)})

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inflection (ln(x-2))/((x-2)^2)

inflection points

\frac{ln ( x - 2 )}{( x - 2 ) ^{2}}

(e^{\frac{5}{6}} + 2, \frac{5}{6 e ^{\frac{5}{3}}})

Solution steps

f^{''} (x) = - \frac{- 6 ln ( x - 2 ) + 5}{( x - 2 ) ^{4}}

Find intervals:

Concave Downward

: 2 < x < e^{\frac{5}{6}} + 2,

Concave Upward

: e^{\frac{5}{6}} + 2 < x < \infty

Plug

x = e^{\frac{5}{6}} + 2

into

\frac{ln ( x - 2 )}{( x - 2 ) ^{2}} : \frac{5}{6 e ^{\frac{5}{3}}}

(e^{\frac{5}{6}} + 2, \frac{5}{6 e ^{\frac{5}{3}}})

What is the inflection (ln(x-2))/((x-2)^2) ?
The inflection (ln(x-2))/((x-2)^2) is (e^{5/6}+2, 5/(6e^{5/3)})