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
Step 1: Convert the decimal to a fraction and simplify. 0.6125 = (6125)/(10000) Divide both numerator and denominator by common factors. (6125)/(10000) = (1225)/(2000) = (245)/(400) = (49)/(80) So, we need to evaluate ((49)/(80)). Step 2: Express the fraction in terms of prime factors. 49 = 7^2 80 = 8 × 10 = 2^3 × (2 × 5) = 2^4 × 5 Therefore, 0.6125 = ((7^2)/(2^4 × 5)) Step 3: Apply logarithm properties. Using the properties ((A)/(B)) = A - B, (A × B) = A + B, and (A^n) = n A: ((7^2)/(2^4 × 5)) = (7^2) - (2^4 × 5) = 2 7 - ( (2^4) + 5) = 2 7 - 4 2 - 5 Step 4: Determine the value of 2. We are given 5 = 0.6990. Assuming base 10 logarithms (standard when no base is specified and values like 0.6990 are given), we know 10 = 1. Since 10 = 2 × 5, we have: 10 = (2 × 5) 1 = 2 + 5 1 = 2 + 0.6990 2 = 1 - 0.6990 2 = 0.3010 Step 5: Substitute the known values and calculate. Given 5 = 0.6990 and 7 = 0.8451. Substitute these values and 2 = 0.3010 into the expression from Step 3: 0.6125 = 2(0.8451) - 4(0.3010) - 0.6990 = 1.6902 - 1.2040 - 0.6990 = 0.4862 - 0.6990 = -0.2128 The final answer is -0.2128. 3 done, 2 left today. You're making progress.