对数不同底数相乘如何运算,(log以4为底3+log以8为底3)*(log3为底2+log9为底2)求教~

对数不同底数相乘如何运算,(log以4为底3+log以8为底3)*(log3为底2+log9为底2)求教~

=(lg3/lg4+lg3/lg8)(lg2/lg3+lg2/lg9
=(lg3/2lg2+lg3/3lg2)(lg2/lg3+lg2/2lg3)
然后用乘法分配率意义乘开，然后约分，答案就为5/4

log(m)n=lgn/lgm。(m是底数） log以根号3为底2的对数=a，求log以12为底3的对数 a=log(√3)2 =lg2/lg3^(1/2) =2lg2/lg3 log（12）3=lg3/lg12=lg3/(2lg2 lg3)=1/(2lg2/lg3 1)=1/(a 1) 已知log以3为底2的对数=a，3的b次方=7，求log以12为底56的对数 a=lg2/lg3；b=log(3)7=lg7/lg3。b/a=lg7/lg2. log(12)56=lg56/lg12 =(lg7 lg8)/(lg3 lg4) =(lg7 3lg2)/(lg3 2lg2) =(lg7/lg2 3)/(lg3/lg2 2) =(b/a 3)/(1/a 2) =(3a b)/(2a 1)

,(log以4为底3+log以8为底3)*(log3为底2+log9为底2) =(log以4为底3+1/2log以4为底3)*(log3为底2+1/2log3为底2) =3/2log以4为底3*3/2log3为底2 =9/4log以4为底3*log3为底2

=[1/2log(2)3+1/3log(2)3]*[log(3)2+1/2log(3)2] =5/6log(2)3*3/2log(3)2 =5/4 结果怎么不是4/5？