SOLUTION: Find the largest value of x that satisfies: log(base2)(x^2)-log(base2)(x+4)=2 I was not able to find the answer, here are my step I tried to solve it. log(base2)(x^2)-log

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Find the largest value of x that satisfies: log(base2)(x^2)-log(base2)(x+4)=2 I was not able to find the answer, here are my step I tried to solve it. log(base2)(x^2)-log      Log On


   

Question 998702: Find the largest value of x that satisfies:
log(base2)(x^2)-log(base2)(x+4)=2
I was not able to find the answer, here are my step I tried to solve it.
log(base2)(x^2)-log(base2)(x+4)=2
log(base2) (x^2)/(x+4)=2
2^2= (x^2)/(x+4)
4= (x^2)/(x+4)
4(x+4)=x^2
4x+16=x^2
sqrt(4x+16)=x
2x+4=x
x=-4
Found 2 solutions by josgarithmetic, Romolo:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
log(base2)(x^2)-log(base2)(x+4)=2

log%282%2C%28x%5E2%29%29-log%282%2C%28x%2B4%29%29=2

log%282%2C%28x%5E2%2F%28x%2B4%29%29%29=2
Base of the exponent AND the logarithm both are 2.
Put into exponential form.

2%5E2=x%5E2%2F%28x%2B4%29

x%5E2=4%28x%2B4%29
x%5E2=4x%2B16
x%5E2-4x-16=0
x=%284%2B-+sqrt%2816%2B4%2A16%29%29%2F2
x=%284%2B-+4sqrt%281%2B4%29%29%2F2
highlight%28x=2%2B-+2sqrt%285%29%29

Answer by Romolo(1) About Me  (Show Source):
You can put this solution on YOUR website!
You were on the right track till 4x+16=x^2
You can't solve sqrt(4x+16)=x
but you must bring all elements to the same side and equate to zero
like this:
x^2-4x-16 = 0
then solve as usual by quadratic equations.
Ciao