Question

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Answer 1

GIVEN

${ (\frac{3}{5} )}^{3} \div ({\frac{625}{81}})^{2x - 1} = \frac{9}{25}$

TO FIND

Value of x

SOLUTION

${ (\frac{3}{5} )}^{3} \div ({\frac{625}{81}})^{2x - 1} = \frac{9}{25} \\ \\ \\ \\ \implies { (\frac{3}{5} )}^{3} \div ({ \frac{ {5}^{4} }{ {3}^{4} } })^{2x - 1} = \frac{ {3}^{2} }{ {5}^{2} } \\ \\ \\ \\ \\ \implies {(\frac{3}{5} )}^{ 3} \div {{(\frac{5}{3} )}^{(4)} }^{2x - 1} = \frac{ {3}^{2} }{ {5}^{2} } \\ \\ \\ \\ \implies {(\frac{3}{5} )}^{ 3} \div { (\frac{5}{3}) }^{8x - 4} = \frac{ {3}^{2} }{ {5}^{2} } \\ \\ \\ \\ \implies {(\frac{3}{5} )}^{ 3} \div { (\frac{3}{5}) }^{4 - 8x} = { (\frac{3}{5} ) }^{2} \\ \\ \\ \\ \implies { (\frac{3}{5}) }^{3 - 4 + 8x} = { (\frac{3}{5} ) }^{2} \\ \\ \\ \\ \\ \implies 3 - 4 + 8x = 2 \\ \\ \\ \implies - 1 + 8x = 2 \\ \\ \\ \implies 8x = 3 \\ \\ \\ \implies \boxed{ \boxed{x = \frac{3}{8} }}$