mpjx.net
当前位置:首页 >> (log4 3+log8 3)*(log3 2+log9 2) >>

(log4 3+log8 3)*(log3 2+log9 2)

用换底公式 原式=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9) =(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3) =[(1/2+1/3)(lg3/lg2)][(1+1/2)(lg2/lg3)] =(1/2+1/3)(1+1/2) =5/4

我会,就是把4变为二的平方,所以就是(6log2+3log8) (2log3+4log3)再分别相乘,得出结果!

(log3 2+log9 2)*(log4 3+log8 3) =(lg2/lg3+lg2/lg9)*(lg3/lg4+lg3/lg8) =(lg2/lg3+lg2/2lg3)*(lg3/2lg2+lg3/3lg2 =3/2*lg2/lg3*5/6*lg3/lg2 =3/2*5/6=5/4

(log3 2+log9 2)*(log4 3+log8 3) =(lg2/lg3+lg2/lg9)*(lg3/lg4+lg3/lg8) =(lg2/lg3+lg2/2lg3)*(lg3/2lg2+lg3/3lg2 =3/2*lg2/lg3*5/6*lg3/lg2 =3/2*5/6=5/4

log(9)2=0.5log(3)2 (log(3)2+log(9)2)=1.5*log(3)2 log(4)3=0.5log(2)3 log(8)3=1/3 log(2)3 log(4)3+log(8)3=5/6log(2)3 (1.5*log(3)2)*(5/6log(2)3)=1.25 log(3)2* log(2)3=1

(log2 3/log2 4+log2 3/log2 8)(log3 5/log3 3+log3 5/log3 9)(log5 2/log5 5+log5 2/log5 25) =[(5log2 3)/6][(3log3 5)/2][(3log5 2)/2] 然后全部换成以2为底的对数得上式=(5/6)(3/2)(3/2)[(log2 3/log2 2)(log2 5/log2 3)(log2 2/log2 5)]...

(log3^2 + log9^2)×(log4^3 + log8^3) =(log3^2+0.5log3^2)×(0.5log2^3+1/3*log2^3) =3/2*log3^2×5/6*log2^3 =5/4

(log3(2) + log9(2)) * (log4(3) + log8(3)) = (lg2/lg3 + lg2/lg9) * (lg3/lg4 + lg3/lg8)) = [lg2/lg3 + lg2/(2lg3)] * [lg3/(2lg2) + lg3/(3lg2)] = [(2lg2+lg2)/(2lg3)] * [(3lg3+2lg3)/(6lg2)] = 3lg2/(2lg3)] * 5lg3/(6lg2) = 3/2 * 5/6 =...

原式=(log3(2)+1/2log3(2))*(2log2(3)+3log2(3))=3/2*5*log2(3)*log3(2)=15/2

网站首页 | 网站地图
All rights reserved Powered by www.mpjx.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com