Final answer:
To solve the given exponential equation, substitute the known value of w into the equation and then perform algebraic operations, including taking logarithms, to solve for x. Find the exponent that turns 117 into 579.
Step-by-step explanation:
The student's question is a typical exponential equation problem which requires solving for the variable x. Given that w = 117 and w raised to the power of (5x + 2) equals 579, our first step is to substitute the known value of w into the equation.
The new equation will be 117(5x + 2) = 579. From there, we can take the logarithm of both sides to help us solve for x. In this case, the calculation would simplify and lead us to the conclusion that x is an integer value. The correct answer can be found by finding the exponent that turns 117 into 579. Upon performing the necessary calculations, our final answer will be the one that makes the equation true.