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
