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kaheart [24]
3 years ago
5

27^x −1 = 9^3x−7 what is X

Mathematics
1 answer:
tigry1 [53]3 years ago
3 0

x is \frac{11}{3}

Step-by-step explanation:

Let us revise some rules of exponents

  • (a^{n})(a^{n})=a^{m+n}
  • \frac{a^{m}}{a^{n}}=a^{m-n}
  • (a^{m})^{n}=a^{mn}
  • a^{m}=a^{n} , then m = n

∵ 27^{x-1}=9^{3x-7}

- Factorize 27 and 9

∵ 27 = 3 × 3 × 3

∴ 27 = 3³

∵ 9 = 3 × 3

∴ 9 = 3²

Substitute them in the equation

∴ (3^{3})^{x-1}=(3^{2})^{3x-7}

- Use the third rule to simplify each side

∴ (3)^{3x-3}=(3)^{6x-14}

- Use the fourth rule

∵ The bases of the two sides are equal

∴ Their exponents are equal

∴ 3x - 3 = 6x - 14

- Subtract 6x from both sides

∴ -3x - 3 = -14

- Add 3 to both sides

∴ -3x = -11

Divide both sides by -3

∴ x = \frac{11}{3}

x is \frac{11}{3}

Learn more:

You can learn more about equations in brainly.com/question/4934417

#LearnwithBrainly

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