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(2^2x+2)(2^3x-7)=2^25

less than a minute read Jun 16, 2024
(2^2x+2)(2^3x-7)=2^25

Solving the Equation (2^(2x+2))(2^(3x-7)) = 2^25

This equation involves exponents and requires understanding of exponent rules to solve. Here's how to break it down:

1. Simplify using exponent rules

  • Product of powers: When multiplying powers with the same base, add the exponents. Therefore:
    • (2^(2x+2))(2^(3x-7)) = 2^(2x+2 + 3x-7) = 2^(5x-5)

2. Set up the equation

Now we have:

  • 2^(5x-5) = 2^25

3. Solve for x

  • Equate the exponents: Since the bases are the same, we can equate the exponents:
    • 5x - 5 = 25
  • Solve for x:
    • 5x = 30
    • x = 6

Solution

Therefore, the solution to the equation (2^(2x+2))(2^(3x-7)) = 2^25 is x = 6.

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