Question

solve for x....
${9}^{x + 2} - 6 \: . \: {3}^{x + 1} + 1 = 0$
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Answer 1

Heyaa...☺☺

$= > {9}^{x + 2} - 6 \times {3}^{x + 1} + 1 = 0 \\ \\ = > take \: \: 3 \: \: common \\ \\ = > 3 {}^{ x + 2} - 2 \times {1}^{x + 1} + 1 = 0 \\ \\ = > {3}^{x + 2} - {2}^{x + 1} + 1 = 0 \\ \\ = > {1}^{ x + 2} + {1}^{x + 1} = 0 \\ \\ = > 1 \: \: will \: \: cut \: \: becoz \: \: common \\ \\ = > x + 2 + x + 1 = 0 \\ \\ = > 2x + 3 = 0 \\ \\ = > x = \frac{ - 3}{2}$

Hope it's correct...✌✌

Thanks...☺☺

Answer 2

Answer:

Step-by-step explanation:

Virtuoso

soln:

Given expression is: 9^(n+2) - 6 x 3^(n+1) + 1 = 0

Rearrange the given expression as below:

9² x 9ⁿ - 6 x 3¹ x 3ⁿ + 1 = 0

or, 81 x (3 x 3)ⁿ - 6 x 3 x 3ⁿ + 1 = 0

or, 81 x 3ⁿ x 3ⁿ - 18 x 3ⁿ + 1 = 0

Let 3ⁿ = k, then the above expression is rewritten as:

81 x k x k - 18 x k + 1 = 0

or, 81k² - 18k + 1 = 0

or, 81k² - 9k - 9k  + 1 = 0

or, 9k(9k - 1) -1(9k -1) = 0

or, (9k - 1)(9k - 1) = (9k - 1)² = 0 

or, k = 1/9

or, 3ⁿ = 1/9 = (9)^-1 = (3²)^-1 = (3)^-2

or, n = - 2

Hence the value of n = - 2

Note: for simplicity I replaced x => n (Multiplication sign and variable(x) looks like same, so don't confuse with x and n)

Hope it helps you

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