log 3x^2 - log x = log (x+5) find x

log 3x^2 - log x  = log
(x+5)

First we will use the algorethim proprties  to
simplify the equation.

We know that: log a - log b = log
a/b

==> log (3x^2)/x  = log
(x+5)

Now simplify
:

==> log 3x = log (x+
5)

Now, we know that:

if log a
= log b   Then,    a = b

==>3x = x+
5

==>3x - x =
5

==> 2x =
5

==> x=
5/2

To check
:

log (3x^2) - log x = log (x+
5)

log (3*25/4) - log 5/2 =
log (5/2 + 5)

log (75/4) -
log(5/2) = log (15/2)

log
(75/4) / (5/2)  = log
(15/2)

log (75/10) = log
(15/2)

log ( 15/2) =
log15/2)