Determine the values of x such that logx x7logx x1 Separate

Determine the value(s) of x such that logx (x7)+logx (x)=1. Separate multiple answers with a comma. (Hint: Consider the domain of a logarithmic function.)

x=     

Solution

given  log_x (x7)+log_x (x)=1

log(a)+log(b)=log(ab)

  log_x (x7)x=1

(x7)x=x¹

x²7x=x

x²8x=0

x(x-8)=0

x=0,x=8

x=0 not in domain of a logarithmic function.

so x =8 is the only answer