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1. If ${(\frac{3}{5})}^{3} {(\frac{3}{5})}^{- 6} = {(\frac{3}{5})}^{2 x - 1}$ then x is equal to ?

A. -2

B. -1

C. 1

D. 2

Solution:

\begin{aligned} {(\frac{3}{5})}^{3} {(\frac{3}{5})}^{- 6} = {(\frac{3}{5})}^{2 x - 1} \\ \Rightarrow {(\frac{3}{5})}^{(3 - 6)} = {(\frac{3}{5})}^{2 x - 1} \\ \Rightarrow {(\frac{3}{5})}^{- 3} = {(\frac{3}{5})}^{2 x - 1} \\ \Rightarrow 2 x - 1 = - 3 \\ \Rightarrow 2 x = - 2 \\ \Rightarrow x = - 1 \end{aligned}

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