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Step-by-step explanation:
We know, 9 to the power of 2 is 81
so it will be 81x
so its 81* a/b/c/d = 27/3 to the power of a/b/c/d +2
Solve for all answered!
Answer:
[tex]\textsf{Option (b) 1/5 is your correct answer.}\\[/tex]
Step-by-step explanation:
[tex] \bf➤ \underline{Given-} \\ [/tex]
[tex] \sf{ {9}^{2x} = \frac{27}{ {3}^{x + 2} } } \\ [/tex]
[tex] \bf ➤\underline{To\: find-} \\ [/tex]
[tex]\textsf{the value of x = ?}[/tex]
[tex] \bf➤ \underline{Solution-} \\ [/tex]
[tex]\textsf{Given expression,}\\[/tex]
[tex] \sf{ {9}^{2x} = \frac{27}{ {3}^{x + 2} } } \\ [/tex]
[tex] \sf{ \implies \: {9}^{2x} \times {3}^{x + 2} = 27} \\ [/tex]
[tex] \sf{ \implies \:( {3}^{2} {)}^{2x} \times {3}^{x + 2} = {3}^{3} } \\ [/tex]
[tex] \sf{ \implies \: {3}^{4x} \times {3}^{x + 2} = {3}^{3} } \\ [/tex]
[tex] \sf{ \implies \: {3}^{4x + x + 2} = {3}^{3} } \\ [/tex]
[tex] \sf{ \implies \: { \cancel3}^{5x + 2} = { \cancel3}^{3} } \\ [/tex]
[tex] \sf{ \implies \: }5x + 2 = 3 \\ [/tex]
[tex] \sf{ \implies \: 5x = 3 - 2} \\ [/tex]
[tex] \sf{ \implies \: 5x = 1} \\ [/tex]
[tex] \sf{ \implies \: x = \frac{1}{5} } \\ [/tex]
[tex] \bf ➤\underline{Answer-} \\ [/tex]
[tex] \bf \underline{Hence, the\: value\: of \:x \: is \: \frac{1}{5}.} \\ [/tex]