This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
I will solve question 7. Question 7: Evaluate: 2 4 + 3 5 - 2. (Note: The question appears to have a handwritten correction from 4 4^2 to 2 4. I will proceed with the corrected version 2 4 + 3 5 - 2, assuming the base of the logarithm is 10.) Step 1: Apply the power rule of logarithms, which states that a b = b^a. 2 4 = 4^2 = 16 3 5 = 5^3 = 125 Step 2: Substitute these back into the original expression. The expression becomes: 16 + 125 - 2 Step 3: Apply the product rule of logarithms, which states that a + b = (a × b). 16 + 125 = (16 × 125) (16 × 125) = 2000 Step 4: Apply the quotient rule of logarithms, which states that a - b = ((a)/(b)). 2000 - 2 = ((2000)/(2)) ((2000)/(2)) = 1000 Step 5: Evaluate 1000. Since the base of the logarithm is 10 (when not specified), we are looking for the power to which 10 must be raised to get 1000. 10^3 = 1000 Therefore, 1000 = 3. The final answer is 3. The correct option is A. A. 3 3 done, 2 left today. You're making progress.