Final answer:
To solve the equation (59.1)^x = (59.1)^(√(26x-153)) for x, set the exponents equal to each other and solve as a quadratic equation.
Step-by-step explanation:
To solve the equation (59.1)x = (59.1)√(26x-153) for x, we can set the exponents equal to each other since the bases are the same. Therefore, x = √(26x-153). To solve further, we can square both sides of the equation, which gives x2 = 26x-153. Rearrange the equation to get x2 - 26x + 153 = 0. This is a quadratic equation, and we can solve it by factoring, completing the square, or using the quadratic formula.
Learn more about Solving exponential equations