log2^25*log3^2倍根号2*log5^9=
问题描述:
log2^25*log3^2倍根号2*log5^9=
答
利用公式lga^b=blga知:
lg25=2lg5,lg9=2lg3,lg2倍根号2=(3/2)*lg2
log2^25*log3^2倍根号2*log5^9 (利用loga^b=lga/lgb,化成同底形式)
=[(lg25)/lg2]*[(lg2倍根号2)/lg3]*lg9/lg5(分母与分母乘,分子与分子乘)
=[2lg5*(3/2)lg2*2lg3]/[lg2*lg3*lg5]
=2*(3/2)*2=6