Question

f(x)=100^x-1=1000 (x-1)lf100=lg1000 (x-1)=3/2

Answer 1

两边取导lg

lg(f(x))=lg(100^x-1)=lg(1000)

lg(f(x))=(x-1).lg(100)=lg(1000)

lg(f(x))=(x-1).lg10^2=lg10^3

(x-1)lg10^2=lg10^3

2(x-1)=3

(x-1)=3/2

x=5/2

f(x)=f(5/2)=1000

f^-1(1000)=5/2