Question

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

Answer 1

Answer:

Value of x=8

Step-by-step 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

Answer 2

Answer:

solution to the equation is 8

Step-by-step explanation: