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

*print*Print*list*Cite

### 3 Answers

first of all u have to open out the brackets by multiplying everything inside the brackets by 4

8x-80=1

then you get the x on one side of the equals sign to be able to find out what x is. to do this you have to add 80 to both sides

+80) 8x=81

then you simply divide 81 by 8 to get x

81/8= 10.125

x=10.125

this is just another method of doing it which might help :)

4(2x-20) = 1

This is a linear equation in one variable x. Such equations are solved by isolating x by simple operarions of adding equals to both sides, subtracting equals from both sides , multiplying or dividing both sides by equals. But never multiply or divide by zero.

4(2x-20) = 1

Divide by 4 both sides.

2x-20 = 1/4

Add 20 to both sides.2x = 1/4+20 = 20.25

Divide by 2 both sides.

x = 20.25/2 = 10.125

x = 10.125 is th solution of the equation.

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.)