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Solve 9^(2x-1)=27 for x

Solve 92x−1=27 9^{2 x-1}=27 for x x

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Full solution

Q. Solve 92x−1=27 9^{2 x-1}=27 for x x
  1. Rewrite as Power of 99: Rewrite 2727 as a power of 99 to make the bases the same.\newline2727 can be written as 939^3.\newlineSo, 92x−1=939^{2x-1} = 9^3.
  2. Set Exponents Equal: Since the bases are the same, set the exponents equal to each other. 2x−1=32x - 1 = 3.
  3. Isolate Term with x: Add 11 to both sides to isolate the term with x.\newline2x−1+1=3+12x - 1 + 1 = 3 + 1.\newline2x=42x = 4.
  4. Solve for x: Divide both sides by 22 to solve for xx.2x2=42\frac{2x}{2} = \frac{4}{2}.x=2x = 2.

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