Question

asked Jun 12, 2023 39.3k views

1 Answer

Kishyr Ramdial · Answer 1 · 2023-06-18T14:19:46+0000

$9 * ( {3}^(n - 2) ) = {27}^(n + 1) \\$

${3}^(2) * {3}^(n - 2) = ({ {3}^(3) })^(n + 1)$

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Hint :

${a}^(b) * {a}^(c) = {a}^(b + c)$

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$({ {a}^(b) })^(c) = {a}^(b * c)$

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${3}^(n - 2 + 2) = {3}^(3 * (n + 1))$

${3}^(n) = {3}^(3n + 3)$

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${a}^(b) = {a}^(c)$

b = c

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n = 3n + 3

Switch sides

3n + 3 = n

Subtract both sides minus 3

3n + 3 - 3 = n - 3

3n = n - 3

Subtract both sides minus n

3n - n = n - n - 3

2n = - 3

Divide both sides by 2

$(2n)/(2) = ( - 3)/(2) \\$

$n = - (3)/(2) \\$