Solve for x: log (x+5) = 2 - log (2x)

log (x+5) = 2- log (2x).

I
believe that you need to determine the values of x that satisfies the
equation.

We will use logarithm properties to solve for
x.

First we will add log 2x to both
sides.

==> log (x+ 5) + log (2x) =
2

Now we know that log a + log b= log
a*b.

==> log (x+5)*2x =
2

==> log ( 2x^2 +10x) =
2

Now we will rewrite into the exponent
form.

==> 2x^2 + 10x =
10^2

==> 2x^2 + 10x =
100

==> 2x^2 + 10 x -100 =
0

Now we will divide by
2.

==> x^2 + 5x -50 =
0

Now we will
factor.

==> (x+10) (x-5) =
0

==> x1= -10 ==> Not valid because log ca
not be negative.)

==> x2=
5

Let us check .

==>
log (5+5) = 2 - log 2*5

==> log 10 = 2- log
10

==> 1 =
2-1

==> 1 = 1

Then the
answer is valid

==> Then the answer is
x= 5.