Question

求值:(log以4为底的3的对数+log以8为底的3的对数)乘（log以3为底的2的对数+log以9为底的2的对数）—

求值:(log以4为底的3的对数+log以8为底的3的对数)乘（log以3为底的2的对数+log以9为底的2的对数）—log以1/2为底的32开四次方的对数

Answer 1

用换底公式
原式=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9)-lg32/lg(1/2)
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)-5lg2/(-lg2)
=(1/2+1/3)(lg3/lg2)(1+1/2)(lg2/lg3)+5
=(5/6)(3/2)+5
=25/4