If 9x-2 - 240 - 9x- then x - 0-20-40-10-5

The correct option is D 0.5 9^x+2 = 240 + 9^x⇒ 9^x+2 9^x = 240 ⇒ 9^x9^2 9^x = 240 ⇒ 9^x (9^2 1)=240 ⇒ 9^x(81 1) = 240 ⇒ 9^x× 80 = 240 ⇒ 9^x = 240/80=3⇒(3^2)^ ...

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Byju's Answer

Standard IX

Mathematics

Laws of Exponents for Real Numbers

If 9x+2 = 240...

Question

If $9^{x + 2} = 240 + 9^{x}$ , then x =

0.5

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Solution

The correct option is A
0.5

$9^{x + 2} = 240 + 9^{x} \Rightarrow 9^{x + 2} - 9^{x} = 240 \Rightarrow 9^{x} 9^{2} - 9^{x} = 240 \Rightarrow 9^{x} (9^{2} - 1) = 240 \Rightarrow 9^{x} (81 - 1) = 240 \Rightarrow 9^{x} \times 80 = 240 \Rightarrow 9^{x} = \frac{240}{80} = 3 \Rightarrow (3^{2})^{x} = 3^{1} \Rightarrow 3^{2 x} = 3^{1} ∴ 2 x = 1 \Rightarrow x = \frac{1}{2} = 0.5$

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If 9x+2=240+9x, then x =

The correct option is A 0.5 9x+2=240+9x⇒9x+2−9x=240⇒9x92−9x=240⇒9x(92−1)=240⇒9x(81−1)=240⇒9x×80=240⇒9x=24080=3⇒(32)x=31⇒32x=31∴2x=1⇒x=12=0.5

If $9^{x + 2} = 240 + 9^{x}$ , then x =