Question

Log(-x-1)=log(5x)-logx

When I solve for x I got -6 but the book answer says no solution.

Can anyone show me why?

@precal

Answer 1

definition of log

Answer 2

x can't be negative

Answer 3

if x = -6, then

log(-x-1) = log(5x) - log(x)

log(-(-6)-1) = log(5(-6)) - log(-6)

log(5) = log(-30) - log(-6)

But you can't take the log of a negative number, so x = -6 isn't part of the domain

Answer 4

But shouldn't it have said -6 is extraneous?

I am concerned that I did the solving steps incorrectly.

Answer 5

no solution and extraneous can be used the same way........