若lg2=a,lg3=b,则log9 40

问题描述:

若lg2=a,lg3=b,则log9 40

log9(40)
=lg40/lg9
=lg(2²×10)/lg3²
=(lg2²+lg10)/(2lg3)
=(2lg2+1)/(2lg3)
=(2a+1)/(2b)