We are given:&nbsp;9x−1=27−x+2Assign a power of 3 to each base:&nbsp;(32)x−1=(33)−x+2Use the rule:&nbsp;(am)n=amn&nbsp;32(x−1)=32(−x+2)Equate the exponents:&nbsp;2(x−1)=3(−x+2)Solve for x:2x−2=−3x+82x=−3x+85x=8x=85&nbsp;or 1.6

Key to "9x−1=27−x+2"

Secondary
Algebra
Algebra I
Quadratic function and equation

Ayaana Buck

Answered question

2021-02-08

9^{x} - 1 = 27^{- x} + 2

Answer & Explanation

diskusje5

Skilled2021-02-09Added 82 answers

We are given: $9^{x} - 1 = 27^{- x} + 2$
Assign a power of 3 to each base: ${(3^{2})}^{x} - 1 = {(3^{3})}^{- x} + 2$
Use the rule: ${(a^{m})}^{n} = a^{m} n$ $3^{2} (x - 1) = 3^{2^{(- x + 2)}}$
Equate the exponents: $2 (x - 1) = 3 (- x + 2)$
Solve for x:
$2 x - 2 = - 3 x + 8$
$2 x = - 3 x + 8$
$5 x = 8$
$x = \frac{8}{5}$ or 1.6

Jeffrey Jordon

Expert2021-08-10Added 2575 answers

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