what is the step by step solution to this problem?
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2 In (x + 4) - In x = In ( x + a)
=> 2 In (x + 4 ) = In ( x + a) + In x
=> In [( x + 4 ) ^2] = In [ ( x + a ) × x ]
(Using ==> a In ( b ) = In ( b ^a) , In( a )+ In( b ) = In (ab) )
Taking 'e' as a base on the both sides we get ,
( x+ 4 ) ^2 = (x + a) × x
=> x^2 + 2 × (x) x (4) + 4^2 = x^2 + ax
( x ^2 cancels from both sides )
=> 8x + 16 = ax
=> ax = 8x + 16
=> ax - 8x = 16
=> x ( a - 8 ) = 16
On divinding both sides by a - 8 gives
x = 16 / a - 8
=> 2 In (x + 4 ) = In ( x + a) + In x
=> In [( x + 4 ) ^2] = In [ ( x + a ) × x ]
(Using ==> a In ( b ) = In ( b ^a) , In( a )+ In( b ) = In (ab) )
Taking 'e' as a base on the both sides we get ,
( x+ 4 ) ^2 = (x + a) × x
=> x^2 + 2 × (x) x (4) + 4^2 = x^2 + ax
( x ^2 cancels from both sides )
=> 8x + 16 = ax
=> ax = 8x + 16
=> ax - 8x = 16
=> x ( a - 8 ) = 16
On divinding both sides by a - 8 gives
x = 16 / a - 8
Nice answer
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