If ab=(ba)1−2x\sqrt{\dfrac{a}{b}} = \Big(\dfrac{b}{a}\Big)^{1 - 2x}ba=(ab)1−2x, the value of x is :
34\dfrac{3}{4}43
35\dfrac{3}{5}53
−34-\dfrac{3}{4}−43
−35-\dfrac{3}{5}−53
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Given,
⇒ab=(ba)1−2x⇒(ab)12=(ba)1−2x⇒(ab)12=(ab)−(1−2x)⇒(ab)12=(ab)(2x−1)⇒12=2x−1⇒2x=1+12⇒2x=2+12⇒x=32×2⇒x=34.\Rightarrow \sqrt{\dfrac{a}{b}} = \Big(\dfrac{b}{a}\Big)^{1 - 2x} \\[1em] \Rightarrow \Big(\dfrac{a}{b}\Big)^{\dfrac{1}{2}} = \Big(\dfrac{b}{a}\Big)^{1 - 2x} \\[1em] \Rightarrow \Big(\dfrac{a}{b}\Big)^{\dfrac{1}{2}} = \Big(\dfrac{a}{b}\Big)^{-(1 - 2x)} \\[1em] \Rightarrow \Big(\dfrac{a}{b}\Big)^{\dfrac{1}{2}} = \Big(\dfrac{a}{b}\Big)^{(2x - 1)} \\[1em] \Rightarrow \dfrac{1}{2} = 2x - 1 \\[1em] \Rightarrow 2x = 1 + \dfrac{1}{2} \\[1em] \Rightarrow 2x = \dfrac{2 + 1}{2} \\[1em] \Rightarrow x = \dfrac{3}{2 \times 2} \\[1em] \Rightarrow x = \dfrac{3}{4}.⇒ba=(ab)1−2x⇒(ba)21=(ab)1−2x⇒(ba)21=(ba)−(1−2x)⇒(ba)21=(ba)(2x−1)⇒21=2x−1⇒2x=1+21⇒2x=22+1⇒x=2×23⇒x=43.
Hence, Option 1 is the correct option.
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If 82x + 5 = 1, value of x is :
−52-\dfrac{5}{2}−25
52\dfrac{5}{2}25
2
25\dfrac{2}{5}52
If 3x + 1 = 9x - 2, the value of x is :
-5
5
0
3
Solve for x :
22x + 1 = 8
25x - 1 = 4 × 23x + 1
