已知log以根号3为底2的对数等于a分之1-a,求log以12为底3的对数的值?

Question

已知log以根号3为底2的对数等于a分之1-a,求log以12为底3的对数的值?

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)