(log2 3+log8 9)(log3 4+log9 8+log3 2)的运算过程关于换底公式的都懂不起哟
问题描述：
(log2 3+log8 9)(log3 4+log9 8+log3 2)的运算过程
关于换底公式的都懂不起哟
答
(log2 3+log8 9)(log3 4+log9 8+log3 2)
=(log2 3+log2^3 3^2)(log3 2^3+log3^2 2^3+log3 2)
=(log2 3+2/3log2 3)(3log3 2+3/2log3 2+log3 2)
=(5/3log2 3)*(11/2log3 2)
=55/6
答
注明一下loga的n次方 b的m次方=(m/n)loga bloga b=lg b/lg a原式=(log2 3+log8 9)(log3 4+log9 8+log3 2)=[log2 3+(2/3)log2 3][2log3 2+(3/2)log3 2+log3 2]=(5/3)log2 3*(9/2)log3 2=(15/2)(lg 3/lg 2)(lg 2/lg 3)...