Respuesta :

Space

Answer:

[tex]x = -23[/tex]

General Formulas and Concepts:

Algebra II

  • Exponential Rules

Step-by-step explanation:

Step 1: Define

[tex]125^{x+5} = 25^{x-4}[/tex]

Step 2: Solve for x

  1. Rewrite:                                        [tex]5^{3(x+5)} = 5^{2(x-4)}[/tex]
  2. Define:                                          [tex]3(x+5) = 2(x-4)[/tex]
  3. Distribute:                                     [tex]3x+15 = 2x-8[/tex]
  4. Subtract 2x on both sides:          [tex]x+15 = -8[/tex]
  5. Subtract 15 on both sides:          [tex]x = -23[/tex]

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