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2log2 3+2log4 3等于多少

使用对数的换底公式,logs(N)=logb(N)/logb(a). log4(3)=log2(3)/log2(4)=1/2*log2(3)=log√3 2log2 3+2log4 3=3log2 3

log2(3)-log4(6) = log2(3)-log2^2((√6)^2) = log2(3)-log2(√6) = log2(3/√6) = log2(√3/√2) = log2(√3)-log2(√2) = 1/2log2(3) - 1/2 如果题目是【log2(3)-log4(36)】 log2(3)-log4(36) = log2(3)-log2^2((6)^2) = log2(3)-log2(6) = log2(3/6)...

log2+log3=log6 如下图所示,是“4”的第一个公式的逆运算

(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

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都换成以2为底的对数进行比较 log2(3)=log2(根号9) log4(5)=log2(根号5) 3/2=log2(2^(3/2))=log2(根号8) 因为y=log2(x)在(0,+无穷)上为增函数 所以log2(3)>3/2>log4(5)

log4(4/3) =lg(4/3)/lg4 =lg(4/3)/2lg2 =lg√(4/3)/lg2 =log2[√(4/3)] 2/3

(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

=(log2 3 +3/2log2 3)(2log3 2+3/2log3 2) =5/2log2 3 ×7/2log3 2 =35/4

log4(12)=1/2log2(12)=log2(√12)所以2的(log4(12))次方=√12=2√3log9(27)=1/2log3(27)=3/2所以3的(log9(27))次方=3^(3/2)=√3??=√27=3√3log25(1/3)=1/2log5(1/3)=log5(√1/3)所以5的(log25(1/3))次方=√1/3=(√3)/3故2的(log4(12))...

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