find the largest value of x

Question

find the largest value of x that satisfies:

log₂(x²)-log₂(x+5)=2

Answer 1

log_a b  −  log_a c  =  log_a (b / c)
log_a x = b  ----->  a^b = x 
~~~~~~~~~~~

log₂ x² − log₂ (x + 5) = 2

log₂ [x² / (x + 5)] = 2 

   x²   
--------  =  2²  
 x + 5

x² = 4(x + 5) 

x² - 4x - 20 = 0

D = (-4)² +80 = 96

x₁₂ = (4 ± √96) / 2

x₁ = 2 + 2√6 > 0

x₂ = 2 − 2√6 < 0 (logarithm is not exist for negative numbers and 0)

x = 2(1 + √6)  is the answer.