Question

d) If (3^2x-1 - 5) ÷ 2 = 11, then the value of
x is
i. 1
ii. 2
iii. 3
iv. 4​

Answer 1

$\huge{ \underbrace{ \text{Correct \: question}}}$

$\sf{If \: ( {3}^{2x - 1} - 5) \div 2 = 11 \: then \:find \: the \: value \: of \: \bold{x}}$

$\huge{ \underbrace{ \text{ Answer}}}$

Given Equation:-

$\sf{ \bold{ ({3}^{2x - 1} - 5) \div 2 = 11}}$

$\\ \sf{ \implies{({3}^{2x - 1} - 5) = 11 \times 2}}$

$\\ \sf{ \implies{{3}^{2x - 1} = 22 + 5}}$

$\\ \sf{ \implies{3 {}^{2x - 1} = 27}}$

$\\ \sf{ \implies{ {3}^{2x - 1} = {3}^{3} }}$

$\\ \sf{ \therefore{2x - 1 = 3}} \: \: \: \boxed{ \sf{ \blue{ \because{ {a}^{x} = {a}^{y} \rightarrow{ x = y}}}}}$

$\\ \sf{ \implies{2x = 3 + 1}}$

$\\ \sf{ \implies{2x = 4}}$

$\\ \sf{ \implies{x = \frac{4}{2} }}$

$\\ \boxed{ \sf{ \implies{ \orange{x = 2}}}}$

$\underline{ \boxed{ \rm{Hence, \: option \: \bold{ ii)2 \: } \: is \: correct. }}}$

$\sf{ \underline{ \underline{ \pink{More \: Identities:-}}}}$

$\sf{ \rightarrow{ \bold{ {a}^{x} + {a}^{y} }}}= {a}^{xy} \\ \\ \sf{ \rightarrow{ \bold{ {a}^{x} \times {a}^{y} }}}= {a}^{x + y} \\ \\ \sf{ \rightarrow{\bold{ {a}^{x} - {a}^{y} }}}= {a}^{x \div y} \\ \\ \sf{ \rightarrow{\bold{ {a}^{x} \div {a}^{y} }}}= {a}^{x - y} \\ \\\sf{ \rightarrow{\bold{( {a}^{x} ) {}^{y} }}} = a {}^{xy} \\ \\ \sf{ \rightarrow{\bold{ {a}^{0} }}} = 1$