Question

$9 ^{x + 2} = 240 + 9 ^{x}$
​

Answer 1

Answer:

Given: 9  

x+2

=240+9  x

⇒9 x+2

−9  x

=240

⇒9  x

(81−1)=240

⇒9  x

=3

⇒3  2x

=3  

1

 ⇒2x=1

⇒x=  2

1

​  

=0.5

Step-by-step explanation:

Answer 2

Step-by-step explanation:

$=⟩ {9}^{x + 2} = 240 + {9}^{x} \\=⟩ {9}^{x + 2} - {9}^{x} = 240 \\ =⟩ {9}^{x} . {9}^{2} - {9}^{x} = 240 \\ =⟩ {9}^{x} ( {9}^{2} - 1) = 240 \\ =⟩ {9}^{x} ( 81- 1) = 240 \\ =⟩ {9}^{x} \times 80 = 240 \\=⟩ {9}^{x} = \frac{240}{80} \\=⟩ {9}^{x} = 3 \\ =⟩ {({3}^{2} )}^{x} = 3 \\ =⟩ {3}^{2x} = {3}^{1} \\ \large{\blue{now \: compare : }}\\=⟩2x=1 \\ =⟩x = \frac{1}{2}$

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