The exact solution for the equation is x= -2.0717
1. Start with the given equation: 2^(2x-1) = 5^(3x+4)
2. Take the logarithm (base 10 or natural logarithm) of both sides to simplify the exponents.
3. Apply logarithm properties to isolate x.
4. The final expression represents the exact solution for x.
5. Solve for x using the properties of logarithms.
6. The solution is x = log(5^4) / (2 * log(2) - 3 * log(5)).
7. This provides the exact value of x that satisfies the original equation.
8. Therefore, the exact solution for the equation is x= -2.0717