Question

please solve this question​

Answer 1

Answer :-

The value of x is - 5/3

Explanation :-

Given :-

$\sf {9}^{x} \times {3}^{2} \times \bigg( {3}^{ -x/2} \bigg) ^{ - 2} = \dfrac{1}{27}$

To find :-

Value of x

Solution :-

$\sf \implies {9}^{x} \times {3}^{2} \times \bigg( {3}^{ -x/2} \bigg) ^{ - 2} = \dfrac{1}{27} \\\\\\ \sf \implies {(3^{2})}^{x} \times {3}^{2} \times \bigg( {3}^{ - x/2} \bigg)^{ - 2} = \dfrac{1}{ {3}^{3} } \\\\\\ \sf \implies 3^{2 \times x} \times {3}^{2} \times {3}^{ - x/2 \times - 2}= \dfrac{1}{ {3}^{3} } \\\\\\ \bf \because ({a}^{m})^{n} = {a}^{mn}\\\\\\ \sf \implies 3^{2x} \times {3}^{2} \times {3}^{x} = \dfrac{1}{ {3}^{3} }\\\\\\ \sf \implies 3^{2x + 2 + x}= \dfrac{1}{ {3}^{3} } \\\\\\ \bf \because {a}^{m} \times {a}^{n} = {a}^{m+n}\\\\\\ \sf \implies 3^{3x + 2} = \dfrac{1}{ {3}^{3} }\\\\\\ \sf \implies 3^{3x + 2}= {3}^{ - 3} \\\\\\ \bf \because \dfrac{1}{ {a}^{n} } = {a}^{ - n} \\\\\\ \sf \implies 3x + 2 = - 3 \\\\\\ \bf \because if \: {a}^{m} = {a}^{n} \: then \: m \: = n \\\\\\ \sf \implies 3x = - 3 - 2 \\\\\\ \sf \implies 3x = - 5 \\\\\\ \sf \implies x = - \dfrac{5}{3}$

Therefore the value of x is - 5/3