1.已知log(9)5=a log(3)7=b 试用ab表示log(21)35

log(21)35=log(21)5+log(21)7
=[1/(log(5)3+log(5)7)]+[1/(log(7)3+log(7)7)]
因为log(9)5=a 所以log(5)3=1/2a
log(3)7=b log(7)3=1/b
所以,原式=(2a/(1+4ba^2))+(b/(1+b))
因为 x^a=y^b=z^c=k
化成对数式,则有：a=log(x)k,b=log(y)k,c=log(z)k
1/a=log(k)x,1/b=log(k)y,1/c=log(k)z
因为 1/a+1/b=1/c,所以有
log(k)x+log(k)y=log(k)xy=log(k)z
所以有 xy=z ,得证。