Question

9^2x=27/3^(x+2) find the value of x​ 2

Answer 1

Step-by-step explanation:

18x=9(x+2)

18x=9x+18

9x=18

x=18/9

x=2

Answer 2

Step-by-step explanation:

$\mathrm{\underline{ \huge{Question - }}}$

$\mathrm{If \: {9}^{2x} = \frac{27}{ {3}^{x + 2} } ,find \: the \: value \: of \: x.}$

$\mathrm{\underline{ \huge{Solution-}} }$

Let's solve!

We have,

$\: \: \: \mathrm{ {9}^{2x} = \frac{27}{ {3}^{x + 2} } }$

$⟹ \mathrm{ {9}^{2x} \times {3}^{x + 2} } = 27$

$⟹ \mathrm{( {3}^{2} {)}^{2x} \times {3}^{x + 2} = {3}^{3} }$

$⟹ \mathrm{{3}^{4x} \times {3}^{x + 2} = {3}^{3} }$

$⟹\mathrm{ {3}^{4x + x + 2} = {3}^{3} }$

$⟹ \mathrm{ {3}^{5x + 2} = {3}^{3} }$

$⟹ \mathrm{5x + 2 = 3}$

$⟹ \mathrm{5x = 3 - 2}$

$⟹ \mathrm{5x = 1}$

$⟹ \mathrm{x = \frac{1}{5} }$

$\mathrm{ \underline{Answer-} \: Hence, the \: value \: of \: x \: is \: \frac{1}{5}. }$

:)