ABC26GN1986 · Surds and Indices
Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
If $2^{2 x-1}+4^{x}=2^{x-\frac{1}{2}}+2^{x+\frac{1}{2}}$, then $x$ equals
(a)$\frac{1}{2}$
(b)$\frac{2}{3}$
(c)$\frac{3}{2}$
(d)1
Answer
Explanation
$2^{2 x-1}+4^{x}=2^{x-\frac{1}{2}}+2^{x+\frac{1}{2}} \Leftrightarrow 2^{2 x-1}+2^{2 x}=2^{x-\frac{1}{2}}+2^{x+\frac{1}{2}}$ $$\begin{aligned} & \Leftrightarrow \quad 2^{(2 x-1)}(1+2)=2^{\left(x-\frac{1}{2}\right)}(1+2) \\ & \Leftrightarrow \quad 2^{(2 x-1)}=2^{\left(x-\frac{1}{2}\right)} \Leftrightarrow 2 x-1=x-\frac{1}{2} \Leftrightarrow x=\frac{1}{2} . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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