Question

急急急急！！求解一道数学题！

求解一道数学题！要有详细过程谢谢！！已知log(以2为底)X乘以log(以3为底)2=1,求X+X平方+X三次方+X四次方+X五次方

Answer 1

log2 (x)*log3 (2)=1
lgx/lg2*lg2/lg3=1
lgx/lg3=1
lgx=lg3
x=3

令s=x+x^2+x^3+x^4+x^5
xs=x^2+x^3+x^4+x^5+x^6
xs-s=x^6-x
s(x-1)=x^6-x
s=(x^6-x)/(x-1)
即x+x^2+x^3+x^4+x^5=(x^6-x)/(x-1)
=（3^6-3)/(3-1)
=(729-3)/2
=363

Answer 2

log2 (x)*log3 (2)=1
lgx/lg2*lg2/lg3=1
lgx/lg3=1
lgx=lg3
x=3

令s=x+x^2+x^3+x^4+x^5
xs=x^2+x^3+x^4+x^5+x^6
xs-s=x^6-x
s(x-1)=x^6-x
s=(x^6-x)/(x-1)
即x+x^2+x^3+x^4+x^5=(x^6-x)/(x-1)
=（3^6-3)/(3-1)
=(729-3)/2
=363