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find the largest value of x

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1 Answer

loga b  −  loga c  =  loga (b / c)
loga x = b  ----->  ab = 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.