What is solution of the equation : log(4x+16) - log100 = log16 - 2*log2

We'll apply quotient rule, both sides of the
equation:

log [(4x+16)/100] =
log(16/4)

Since the bases are matching, we'll apply one to
one property:

[(4x+16)/100] =
16/4

[(4x+16)/100] = 4

We'll
multiply by 100 both sides:

4x + 16 =
4*100

We'll divide by 4:

x + 4
= 100

We'll subtract 4:

x =
100 - 4

x = 96

The constraint
of existence of logarithm is
4x+16>0

4x>-16

x>-4

The
interval of admissible values for x is (-4 ;
+infinite).

Since the value of x is in the
rangle of admissible values, we'll accept as solution of the equation x =
96.