Question

The solution to the equation log2x + log2(x – 6) = 4 is x =

Answer 1

solution to the equation is 8

Explanation:

Answer 2

Value of x=8

Explanation:

Given :
`log_2x+log_2(x-6)=4`

To find : The solution to the equation given

Solution :

Step 1- Write the given expression

`log_2x+log_2(x-6)=4`

Step 2 - Using logarithmic laws

`log_(b)x+log_by=log_bxy`

`log_2(x)(x-6)=4`

Step 3 - To remove log-base 2, we need to raise the left and right hand terms to power 2.

`(x)(x-6)=2^4`

`x^2-6x-16=0`

Step 4 - Solve the quadratic equation

`x^2-8x+2x-16=0`

`x(x-8)+2(x-8)=0`

`(x-8)(x+2)=0`

Either x=8 or x=-2

We neglect x=-2 because negative value is not defined in log.

Value of x=8