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(5n-12)^3=27

2 min read Jun 16, 2024
(5n-12)^3=27

Solving the Equation (5n - 12)^3 = 27

This article will guide you through the steps to solve the equation (5n - 12)^3 = 27.

Understanding the Equation

The equation involves a cube, meaning a number multiplied by itself three times. We need to isolate the variable 'n' to find its value.

Steps to Solve:

  1. Find the cube root of both sides: Since the left side of the equation is cubed, we need to take the cube root of both sides to get rid of the exponent:

    ∛[(5n - 12)^3] = ∛27

    This simplifies to:

    5n - 12 = 3

  2. Solve for 'n':

    • Add 12 to both sides of the equation:
      5n = 15
    • Divide both sides by 5:
      n = 3

Solution

Therefore, the solution to the equation (5n - 12)^3 = 27 is n = 3.

Verification

To verify our solution, we can substitute n = 3 back into the original equation:

(5 * 3 - 12)^3 = (15 - 12)^3 = 3^3 = 27

This confirms that our solution is correct.

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