Question

log2^3=a,3^b=7,a、b表示log12^56

Answer 1

解：
log2^3=a，则lg3/lg2=a
lg3=alg2
3^b=7，则log3^7=b
lg7/lg3=b
lg7=blg3=ablg2
log12^56=lg56/lg12
=(lg7+lg8)/(lg3+lg4)
=(lg7+3lg2)/(lg3+2lg2)
=(ablg2+3lg2)/(alg2+2lg2)
=(ab+3)/(a+2)

追问

=(ablg2+3lg2)/(alg2+2lg2)
=(ab+3)/(a+2) 怎么变哒

追答

lg7=blg3=ablg2
lg3=alg2
我前面解出来了啊，代入=(lg7+3lg2)/(lg3+2lg2)
不就是=(ablg2+3lg2)/(alg2+2lg2)吗？
=(ablg2+3lg2)/(alg2+2lg2)
=［(ab+3)lg2］/［(a+2)lg2］
=(ab+3)/(a+2)【分子分母都有lg2，约去】