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5x+2=1255^{x+2} = 125

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Full solution

Q. 5x+2=1255^{x+2} = 125
  1. Recognize Power of 55: Recognize that 125125 is a power of 55. 125125 is equal to 535^3 because 5×5×5=1255 \times 5 \times 5 = 125.
  2. Write as Power of 55: Write 125125 as a power of 55 in the equation.\newlineReplace 125125 with 535^3 in the equation: 5x+2=535^{x+2} = 5^3.
  3. Set Exponents Equal: Set the exponents equal to each other.\newlineSince the bases are the same 55, we can set the exponents equal to each other: x+2=3x + 2 = 3.
  4. Solve for x: Solve for x.\newlineSubtract 22 from both sides of the equation to solve for x: x=3−2x = 3 - 2.
  5. Calculate xx: Calculate the value of xx.x=1x = 1.

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