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3^x + 7^x = 10^x

Question

3^x + 7^x = 10^x

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Solution

This equation is not solvable using elementary algebraic methods. It is a transcendental equation and it requires numerical methods or special functions to solve.

However, we can make some observations:

  1. If x = 0, then 3^0 + 7^0 = 10^0, which means 1 + 1 = 1, which is not true. So, x ≠ 0.

  2. If x = 1, then 3^1 + 7^1 = 10^1, which means 3 + 7 = 10, which is true. So, x = 1 is a solution.

For other values of x, you would need to use numerical methods or special functions to solve the equation.

This problem has been solved

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