Question

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Answer 1

Given : $\sf{Expression:\bigg(\dfrac{11}{9}\bigg)^{3} × \bigg(\dfrac{11}{9}\bigg)^{6}=\bigg(\dfrac{11}{9}\bigg)^{2x-1}}\:\:$

Need To Find : The Value of x .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\bigstar\sf{ \bigg(\dfrac{11}{9}\bigg)^{3} × \bigg(\dfrac{11}{9}\bigg)^{6}=\bigg(\dfrac{11}{9}\bigg)^{2x-1}}\:\:$

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Solving \: the \: Given \: Expression \::}}$

$:\implies \sf{ \bigg(\dfrac{11}{9}\bigg)^{3} × \bigg(\dfrac{11}{9}\bigg)^{6}=\bigg(\dfrac{11}{9}\bigg)^{2x-1}}\:$

As ,we know that ,

• $a^m \times a^n = a ^{m + n}$

$:\implies \sf{ \bigg(\dfrac{11}{9}\bigg)^{3+6} =\bigg(\dfrac{11}{9}\bigg)^{2x-1}}\:$

$:\implies \sf{ \bigg(\dfrac{11}{9}\bigg)^{9} =\bigg(\dfrac{11}{9}\bigg)^{2x-1}}\:$

Therefore :

$:\implies \sf{9 = 2x-1 }\:\\\\:\implies \sf{2x = 9+1 }\:\\\\:\implies \sf{2x = 10 }\:\\\\:\implies \sf{x = \cancel {\dfrac{10}{2}} }\:\\\\\underline {\boxed{\pink{ \mathrm {  x = 5\: }}}}\:\bf{\bigstar}$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {Hence,\:The  \:value \:of\:x \:is\:\bf{5\: }}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Answer 2

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

As bases are same there fore equation formed

$\hookrightarrow \sf3 + 6 = 2x - 1$

$\hookrightarrow \sf9= 2x - 1$

$\hookrightarrow \sf9 + 1= 2x$

$\hookrightarrow \sf10= 2x$

$\hookrightarrow \sf \: x = \frac{10}{2}$

$\hookrightarrow \boxed{ \frak{\: x = 5} }$

$\therefore\underline \textsf{Value of is\textbf{ 5}}$

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