已知3的a次方=5,3的次方a+b=35,3的c次方=11,3的d次方=77,试证:)

问题描述:

已知3的a次方=5,3的次方a+b=35,3的c次方=11,3的d次方=77,试证:)

35=5*7
3^(a+b)=3^a*3^b
3^b=7
77=11*7
3^d=3^c*3^b
d=c+b

3^a = 5,3^(a + b) = 35,3^c = 11,3^d = 77
log(3,5) = a,(log以3为底,5的对数)
log(3,35) = a + b,b = log(3,35) - log(3,5) = log(3,35/5) = log(3,7)
c = log(3,11),d = log(3,77)
b + c = log(3,7) + log(3,11) = log(3,7*11) = log(3,77) = d

(过程中log全是以3为底的)
因为3的a次方=5,3的次方a+b=35,3的c次方=11,3的d次方=77
所以a=log5,a+b=log35,c=log11,d=log77
因为b+c=a+b+c-a=log35+log11-log5=log(35×11÷5)=log77=d

因为3的a+b次方=35,3的a次方=5
所以3的b次方=35/5=7
因为77=11*7
所以3的d次方=3的b次方*3的c次方
所以b+c=d

3^a=5
3^(a+b)=35
3^c=11
3^d=77
因为(35/5)*11=77
所以[3^(a+b)/3^a]*3^c=3^d
即3^(b+c)=3^d
得到b+c=d

3^a=5
3^(a+b)=35
3^c=11
3^d=77
(35/5)*11=77
[3^(a+b)/3^a]*3^c=3^d
3^(b+c)=3^d
b+c=d