Answer:
Value of x=8
Step-by-step explanation:
Given : [tex]log_2x+log_2(x-6)=4[/tex]
To find : The solution to the equation given
Solution :
Step 1- Write the given expression
[tex]log_2x+log_2(x-6)=4[/tex]
Step 2 - Using logarithmic laws
[tex]log_{b}x+log_by=log_bxy[/tex]
[tex]log_2(x)(x-6)=4[/tex]
Step 3 - To remove log-base 2, we need to raise the left and right hand terms to power 2.
[tex](x)(x-6)=2^4[/tex]
[tex]x^2-6x-16=0[/tex]
Step 4 - Solve the quadratic equation
[tex]x^2-8x+2x-16=0[/tex]
[tex]x(x-8)+2(x-8)=0[/tex]
[tex](x-8)(x+2)=0[/tex]
Either x=8 or x=-2
We neglect x=-2 because negative value is not defined in log.
Value of x=8
Answer:
solution to the equation is 8
Step-by-step explanation:
