exo7 5100

$(**)\;\ln|x+1|-\ln|2x+1|\leq\ln2$,

$(*)\;x^{\sqrt{x}}=\sqrt{x}^x$,

$(**)\;2\Argsh x=\Argch3-\Argth\frac{7}{9}$,

$(**)\;\mbox{ln}_x(10)+2\mbox{ln}_{10x}(10)+3\mbox{ln}_{100x}(10)=0$,

$(**)\;2^{2x}-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}$.