(2011•普陀区三模)已知函数f(x)=ax+x-b的零点x0∈(k,k+1)(k∈Z),且常数a,b分别满足2a=3,3b=2,则k=( ) A.-1 B.0 C.1 D.2
问题描述:
(2011•普陀区三模)已知函数f(x)=ax+x-b的零点x0∈(k,k+1)(k∈Z),且常数a,b分别满足2a=3,3b=2,则k=( )
A. -1
B. 0
C. 1
D. 2
答
∵2a=3,3b=2
∴a=log23,b=log32,
∴函数f(x)=(log23)x+x-log32,且函数是R上的增函数,
而f(-1)=-1<0,f(0)=1-log32>0,
∴函数f(x)=(log23)x+x-log32在(-1,0)内有一个零点
故k=-1,
故选A.