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(-3/4)^2x-1=-27/64

less than a minute read Jun 16, 2024
(-3/4)^2x-1=-27/64

Solving the Equation (-3/4)^(2x-1) = -27/64

This problem involves solving an exponential equation. Here's how to break it down:

1. Expressing Both Sides with the Same Base

  • Simplify the right side: -27/64 can be expressed as (-3/4)³.
  • Rewrite the equation: Now, the equation becomes: (-3/4)^(2x-1) = (-3/4)³

2. Equate the Exponents

Since the bases are the same, we can equate the exponents: 2x - 1 = 3

3. Solve for x

  • Add 1 to both sides: 2x = 4
  • Divide both sides by 2: x = 2

Solution

Therefore, the solution to the equation (-3/4)^(2x-1) = -27/64 is x = 2.

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