Question

solve the following question

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Answer 1

Step-by-step explanation:

$( \frac{11}{9} )^{3} \times ( \frac{9}{11} )^{6} = ( \frac{11}{9} )^{2x - 1}$

$\rm( \frac{11}{9} )^{3} \times ( \frac{11}{9} )^{ - 6} = ( \frac{11}{9} )^{2x - 1} \: [ \because \: \frac{m}{n} = ( \frac{n}{m} )^{ - 1} ]$

$\rm( \frac{11}{9} )^{3 - 6} = ( \frac{11}{9} )^{2x - 1} \: [ \because \: {a}^{m} \times {a}^{n} = ({a})^{m + n} ]$

$\rm( \frac{11}{9} )^{ - 3} = ( \frac{11}{9} )^{2x - 1} \:$

On comparing the powers:-

$\rm - 3 = 2x - 1$

$\rm - 3 + 1= 2x$

$\rm - 2= 2x$

$\rm \frac{ - 2}{2} = x$

$\rm - 1 = x$

$\rm or \: \: \: x = - 1$

I hope it is helpful