关于数学对数的换底公式推论的问题
关于数学对数的换底公式推论的问题
已知 log(2)(3) = a,log(3(7)=b,用a,b表示log(42)(56)
因为log(2)(3)=a,则1/a=log(3)(2),又∵log(3)(7)=b,
∴log(42)(56)=log(3)(56)/log(3)(42)=log(3)(7)+3·log(3)(2)/log(3)(7)+log(3)(2)+1=ab+3/ab+b+1
因为我都四年多没接触过咯···完全忘咯原理是怎样的···请高手帮帮忙仔细的讲解一下下··谢谢··特别是log(3)(7)+3·log(3)(2)/log(3)(7)+log(3)(2)+1=ab+3/ab+b+1
···这里完全不明白用的是什么方法解的···?
运用了如下公式：log(a)(b)/log(a)(c)=log(c)(b)
log(a)(b)=ln(b)/ln(a)
log(a)(b)+log(a)(c)=log(a)(bc)谢谢··可能我没把我的问题说清楚吧··我想问的是··log(3)(7)+3·log(3)(2)为什么会=ab+3而不是=b+3a··········log(3)(7)+log(3)(2)+1为什么会=ab+b+1而不是=b+a+1这样吧，我帮你推导一遍：原式=log（3）（56)/log(3)(42)=(log(3)(7)+log(3)(8))/(log(3)(7)+log(3)(6))=(log(3)(7)+3log(3)(2))/(1og(3)(7)+log(3)(3)+log(3)(2))=(b+3/a)/(b+1+1/a)=(ab+3)/(ab+a+1)你说的log(3)(7)+3·log(3)(2)=b+3/a ·log(3)(7)+log(3)(2)+1=b+1+1/a再补充几个公式：log(a)(b^k)=klog(a)(b)log(a)(b)=1/(log(b)(a))懂？