Solve :
3x - 1 × 52y - 3 = 225
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Solving the expression :
⇒3x−1×52y−3=225⇒3x.3−1×52y.5−3=32×52⇒3x31×52y53=32×52⇒3x×52y=32×52×31×53⇒3x×52y=32+1×52+3⇒3x×52y=33×55⇒x=3 and 2y=5⇒x=3 and y=52=212.\Rightarrow 3^{x - 1} \times 5^{2y - 3} = 225 \\[1em] \Rightarrow 3^x.3^{-1} \times 5^{2y}.5^{-3} = 3^2 \times 5^2 \\[1em] \Rightarrow \dfrac{3^x}{3^1} \times \dfrac{5^{2y}}{5^3} = 3^2 \times 5^2 \\[1em] \Rightarrow 3^x \times 5^{2y} = 3^2 \times 5^2 \times 3^1 \times 5^3 \\[1em] \Rightarrow 3^x \times 5^{2y} = 3^{2 + 1} \times 5^{2 + 3} \\[1em] \Rightarrow 3^x \times 5^{2y} = 3^3 \times 5^5 \\[1em] \Rightarrow x = 3 \text{ and } 2y = 5 \\[1em] \Rightarrow x = 3 \text{ and } y = \dfrac{5}{2} = 2\dfrac{1}{2}.⇒3x−1×52y−3=225⇒3x.3−1×52y.5−3=32×52⇒313x×5352y=32×52⇒3x×52y=32×52×31×53⇒3x×52y=32+1×52+3⇒3x×52y=33×55⇒x=3 and 2y=5⇒x=3 and y=25=221.
Hence, x = 3 and y = 2122\dfrac{1}{2}221.
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Evaluate :
[(−23)−2]3×(13)−4×3−1×16\Big[\Big(-\dfrac{2}{3}\Big)^{-2}\Big]^3 \times \Big(\dfrac{1}{3}\Big)^{-4} \times 3^{-1} \times \dfrac{1}{6}[(−32)−2]3×(31)−4×3−1×61
Simplify :
3×9n+1−9×32n3×32n+3−9n+1\dfrac{3 \times 9^{n + 1} - 9 \times 3^{2n}}{3 \times 3^{2n + 3} - 9^{n + 1}}3×32n+3−9n+13×9n+1−9×32n
If (a−1b2a2b−4)7÷(a3b−5a−2b3)−5=ax.by\Big(\dfrac{a^{-1}b^2}{a^2b^{-4}}\Big)^7 ÷ \Big(\dfrac{a^3b^{-5}}{a^{-2}b^3}\Big)^{-5} = a^x.b^y(a2b−4a−1b2)7÷(a−2b3a3b−5)−5=ax.by, find x + y.
If 3x + 1 = 9x - 3, find the value of 21 + x.
