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Ratio problem of mathematical logarithmic function
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Constructor y=lnx/x

y'=[(lnx)'x-x'lnx]/x? =( 1-lnx)/x?

When x> Iraq, Iraq

So f(x)=lnx/x is a decreasing function on (e, +∞).

x+a & gt; a & gte

So f (x+a) < f(a)

That is ln (x+a)/(x+a) < lna/a.

So AlN (x+a) < (a+x)lna.