Question

find the x and the number is in power​

Answer 1

$\underline{ \huge\bf\red{QuestiOn} :}$

Find X from the given expression :

$\boxed{ {(5)}^{(2x - 1)} = \frac{1}{ {(125)}^{(x - 3)} } }$

$\underline{ \: \huge\bf\green{SolutiOn} \: :}$

We have,

$\begin{aligned} \displaystyle \qquad {(5)}^{(2x - 1)} & = \frac{1}{ {(125)}^{(x - 3)} } \\ \\ \implies {5}^{(2x - 1)} & = \frac{1}{ {5}^{(3)(x - 3)} } \\ \\ & = \frac{1}{ {5}^{(3x - 9)} } \\ \\ & = {5}^{ - (3x - 9)} \\ \\ \implies {5}^{(2x - 1)} & = {5}^{(9 - 3x)} \\ \\ \implies2x - 1& = 9 - 3x \\ & \qquad \sf[comparing \: both \: the \: sides] \\ \\ \implies3x + 2x & = 9 + 1 \\ \\ \implies5x &= 10 \\ \\ \implies \quad& \boxed{ \bf x = 2} \end{aligned}$

$\red{\rule{5.8cm}{0.02cm}}$

$\mid \underline{\underline{\LARGE\bf\green{Brainliest \: Answer}}}\mid$

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