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(2^x+4)^x-3=0 5^x*4^x-4

3 min read Jun 16, 2024
(2^x+4)^x-3=0 5^x*4^x-4

Solving the Equation: (2^x + 4)^x-3 = 0 and 5^x * 4^x - 4

This article will delve into solving the equation (2^x + 4)^x-3 = 0 and exploring its relationship with the expression 5^x * 4^x - 4.

Understanding the Equation (2^x + 4)^x-3 = 0

The equation (2^x + 4)^x-3 = 0 presents a unique challenge due to its exponential structure. To solve it, we'll follow these steps:

  1. Focus on the Base: The key to solving this equation is recognizing that for any non-zero base raised to a power to equal zero, the exponent must be zero. Therefore, we have: x - 3 = 0

  2. Solving for x: Solving this simple linear equation, we find: x = 3

Exploring the Expression 5^x * 4^x - 4

Now let's examine the expression 5^x * 4^x - 4, which is not an equation but a simplified algebraic expression. We can use the solution for x from the previous equation to evaluate this expression:

  1. Substituting x: We substitute x = 3 into the expression: 5^3 * 4^3 - 4

  2. Simplifying: Evaluating the powers, we get: 125 * 64 - 4 = 8000 - 4 = 7996

Conclusion

The solution to the equation (2^x + 4)^x-3 = 0 is x = 3. Using this solution, we found that the expression 5^x * 4^x - 4 evaluates to 7996.

It's important to note that while we found a solution for the equation, this solution might not be the only one. Further analysis might reveal other potential solutions.

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