log以3为底2的对数log以4为底3的对数谁大

Question

如题所述

Answer 1

log(m)n=lgn/lgm。(m是底数）
log以根号3为底2的对数=a，求log以12为底3的对数
a=log(√3)2
=lg2/lg3^(1/2)
=2lg2/lg3
log（12）3=lg3/lg12=lg3/(2lg2
lg3)=1/(2lg2/lg3
1)=1/(a
1)
已知log以3为底2的对数=a，3的b次方=7，求log以12为底56的对数
a=lg2/lg3；b=log(3)7=lg7/lg3。b/a=lg7/lg2.
log(12)56=lg56/lg12
=(lg7
lg8)/(lg3
lg4)
=(lg7
3lg2)/(lg3
2lg2)
=(lg7/lg2
3)/(lg3/lg2
2)
=(b/a
3)/(1/a
2)
=(3a
b)/(2a
1)