Solve log base 4 (x² + x) - log base 4 (x + 1) = 2.
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Answer:
Domain of the function:
x
2
+x>0 and x+1>0
⇒x(x+1)>0⇒x ∈ (−∞, −1)∪(0, ∞)
And x+1>0⇒x∈(−1, ∞)
Taking intersection, we have
⇒x∈(0, ∞)
Now,
log
4
(x
2
+x)−log
4
(x+1)=2
⇒log
4
(
x+1
x
2
+x
)[∵loga−logb=log
b
a
]=2
⇒
x+1
x(x+1)
=4
2
=16
⇒x=16
Ans: D
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