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| 1. |
Solve log base 4 (x² + x) - log base 4 (x + 1) = 2. |
| 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+1x 2 +x )[∵loga−logb=log ba ]=2⇒ x+1x(x+1) =4 2 =16⇒x=16Ans: D | |