Find the value of x; if:
1(125)x−7=52x−1\dfrac{1}{(125)^{x-7}}=5^{2x-1}(125)x−71=52x−1
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1(125)x−7=52x−1⇒1(53)x−7=52x−1⇒1(5)3(x−7)=52x−1⇒153x−21=52x−1⇒(15)3x−21=52x−1⇒5−(3x−21)=52x−1⇒5−3x+21=52x−1⇒−3x+21=2x−1⇒1+21=2x+3x⇒22=5x⇒x=225\dfrac{1}{(125)^{x-7}}=5^{2x-1}\\[1em] \Rightarrow \dfrac{1}{(5^3)^{x-7}}=5^{2x-1}\\[1em] \Rightarrow \dfrac{1}{(5)^{3(x-7)}}=5^{2x-1}\\[1em] \Rightarrow \dfrac{1}{5^{3x-21}}=5^{2x-1}\\[1em] \Rightarrow \Big(\dfrac{1}{5}\Big)^{3x-21}=5^{2x-1}\\[1em] \Rightarrow 5^{-(3x-21)}=5^{2x-1}\\[1em] \Rightarrow 5^{-3x+21}=5^{2x-1}\\[1em] \Rightarrow -3x + 21 = 2x - 1\\[1em] \Rightarrow 1 + 21 = 2x + 3x\\[1em] \Rightarrow 22 = 5x\\[1em] \Rightarrow x = \dfrac{22}{5}(125)x−71=52x−1⇒(53)x−71=52x−1⇒(5)3(x−7)1=52x−1⇒53x−211=52x−1⇒(51)3x−21=52x−1⇒5−(3x−21)=52x−1⇒5−3x+21=52x−1⇒−3x+21=2x−1⇒1+21=2x+3x⇒22=5x⇒x=522
If 1(125)x−7=52x−1\dfrac{1}{(125)^{x-7}}=5^{2x-1}(125)x−71=52x−1 then x=225x = \dfrac{22}{5}x=522
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Evaluate:
[{(−13)−2}2]−1\Big[\Big{\Big(-\dfrac{1}{3}\Big)^{-2}\Big}^2\Big]^{-1}[{(−31)−2}2]−1
5n+2−5n+15n+1\dfrac{5^{n+2}-5^{n+1}}{5^{n+1}}5n+15n+2−5n+1
(23)3×(23)−4=(23)2x+1\Big(\dfrac{2}{3}\Big)^3 \times \Big(\dfrac{2}{3}\Big)^{-4} = \Big(\dfrac{2}{3}\Big)^{2x+1}(32)3×(32)−4=(32)2x+1
4n÷4−3=454^n ÷ 4^{-3} = 4^54n÷4−3=45
