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(1/3)^x=243

2 min read Jun 16, 2024
(1/3)^x=243

Solving the Equation: (1/3)^x = 243

This article will guide you through the steps of solving the equation (1/3)^x = 243.

Understanding the Equation

The equation involves an exponential function where the base is (1/3) and the exponent is 'x'. Our goal is to find the value of 'x' that satisfies the equation.

Solving the Equation

  1. Express 243 as a power of 3: We know that 243 is equal to 3 raised to the power of 5 (3^5 = 243).

  2. Rewrite the equation: Now we can rewrite the equation as: (1/3)^x = 3^5

  3. Express (1/3) as a negative power of 3: Using the rule (a^-n) = 1/(a^n), we can write (1/3) as 3^-1. So the equation becomes: (3^-1)^x = 3^5

  4. Simplify using exponent rules: Applying the rule (a^m)^n = a^(m*n), we get: 3^(-x) = 3^5

  5. Equate the exponents: Since the bases are the same, we can equate the exponents: -x = 5

  6. Solve for x: Multiplying both sides by -1, we get: x = -5

Conclusion

Therefore, the solution to the equation (1/3)^x = 243 is x = -5.

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