What is the solution of the equation log 4 (2x-20) = 1

Before solving the equation, we have to impose constraints
of existance of logarithm
function.

2x-20>0

We'll
add 20 both sides:

2x>20We'll divide by
2:

x>10

So, for the
logarithms to exist, the values of x have to be in the interval (10,
+inf.)

Now, we'll solve the
equation:

2x-20= 4^1

2x-20 =
4

We'll add 20 both sides:

2x
= 20+4

2x = 24

We'll divide by
2:

x =
12

The solution is admissible because the
value belongs to the interval (10,+inf.)