Solve for x if log (x^2) - log 2x = 2.

To solve for x if log (x^2) - log 2x =
2.

Solution:

By property of
logarithms, log(a^m) = m * log a ,

 log a+ log b=
log ab  and

log a = log  b =
log (a/b).

So log x^2 - log2x = 2 = log 10^2, as log10^2 =
2log 10 = 2.

log (x^2 )/(2x) = log
10^2.

We take anti
logarithms:

x^2/(2x) =
100.

x^2 = 200x.

x^2-200x =
0.

x(x-200) = 0.

x = 0, or x=
200.

For x= 0, log(x) is undefined. So x= 200 is a valid
solution.

x =
200.