求log₂25×log₃2√2×log(5)9的结果,

求log₂25×log₃2√2×log(5)9的结果,
求log₂25×log₃2√2×log(5)9的结果,

求log₂25×log₃2√2×log(5)9的结果,
log₂25=log₂5^2 =2log₂5=2log5 / log2
log₃2√2=log₃2^(3/2)=(3/2)log₃2=(3/2)*(log2 /log3)=3log2 /2log3
log(5)9=log(5)3^2=2log(5)3 =2*(log3/log5)=2log3 /log5
所求=2log5 / log2 * 3log2 /2log3 *2log3 /log5 =6...ans

log₂25×log₃2√2×log(5)9
=2log₂5×(3/2)log₃2×(log₂9/log₂5)
=3log₃2×2log₂3
=6