1.（1）.已知lg2=a,lg3=b,试用a,b表示log12^5

1.(1) log12^5=lg5/lg12=1/(lg2*lg12)=1/(lg2*(lg3+2lg2))=1/(a*(b+2a))=1/(ab+2a^2)
(2) 由log2^3=a log3^7=b可以得到log2^7=ab
log14^56=(lg7+3lg2)/(lg7+lg2)=1+2lg2/(lg7+lg2)=1+2/(log2^7+1)=1+2/(ab+1)
2.(1) 因为f(x)=3^x 所以f(x)*f(y)=3^x *3^y=3^(x+y)=f(x+y) 证毕
(2) 同理 f(x)/f(y)=3^x/3^y=3^(x-y)=f(x-y) 证毕