Question

Q.6. If 9^(x+2) = 240 + 9^x , then x
a0.5
b)0.4
c)0.2
d)0.1​

Answer 1

Answer:

x= 1/2

Step-by-step explanation:

9^(x+2) = 240 + 9^x

9^x (9²) =240 + 9^x

9^x (9²) - 9^x = 240

9^x [9²-1] = 240

9^x [81 - 1] = 240

9^x [80] = 240

9^x =240/80

9^x = 3

3^(2x) = 3

By comparing the powers of like base

2x= 1

x = 1/2

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Answer 2

Answer:

0.5

Step-by-step explanation:

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