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[slim timber]

Is this Chinese?

I think you can defferential the equation and then solve it.

The answer can be 1+sqrt(2)/2

[latent halo]

,rccw

[latent halo]

(I) think about the graphical meaning of the quantities on both sides

https://www.desmos.com/calculator/djfkekbict

as $\xi$ increases from 1 to 2, the left region's area increases from 0 to $f(2) > 0$, and the right rectangle's area varies from $e$ to 0.

[fallen phoenix]

vin100

[latent halo]

so we expect to find a point $\xi \in (1,2)$ somewhere in the middle, so that the two areas are equal.

[fallen phoenix]

vin100

[latent halo]

try to capture this idea using some nice properties of the given function.

[latent halo]

II: hint: to use the MVT (mean value theorem), separate known quantities and unknown factors (involving $\eta$) into two sides.

[fallen phoenix]

vin100

[latent halo]

try thinking a way to write the fraction f(2)/ln(2) as a difference quotient.