Question

The solving for the equation of... is -8 an extraneous solution?

Answer 1

I get +-8 for the equation \[2\log_{5}x=3\log_{5}4 \] Is -8 an extraneous solution?

Answer 2

you cant have negative inside the log (there is no exponent for 5 that will make it negative)

Answer 3

I though about that but when I square -8 it equals 64, right. Couldn't I say \[\log_{5}(x^2) \]

Answer 4

\[2\log_{5}(x)=\log_{5}(x^2) \]
is only true if x>0