Exponents

We are given that: From the equation , taking the logarithm base 10 of both sides: Similarly, from , we get: Now we can use these relationships to express and calculate . After calculation, the final result is .

Let , then , and the equation becomes: Rearranging: Factoring the quadratic equation: Thus, or . Since , we have: Therefore, the solutions are and .

We start by simplifying the expression : Now the expression becomes: Using the laws of exponents and , we combine the exponents: Thus, , so the correct answer is (D) 4.