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
Hey Dery, good to see you again. Step 1: Express 0.24 as a fraction. 0.24 = (24)/(100) Step 2: Apply the logarithm quotient rule, ((a)/(b)) = a - b. _10 0.24 = _10 ((24)/(100)) = _10 24 - _10 100 Step 3: Factorize 24 into its prime factors and simplify _10 100. 24 = 2^3 × 3 _10 100 = _10 10^2 = 2 _10 10 = 2 × 1 = 2 Step 4: Substitute these into the expression. _10 0.24 = _10 (2^3 × 3) - 2 Step 5: Apply the logarithm product rule, (ab) = a + b, and the power rule, (a^n) = n a. _10 (2^3 × 3) - 2 = _10 (2^3) + _10 3 - 2 = 3 _10 2 + _10 3 - 2 Step 6: Substitute the given values _10 2 = 0.3010 and _10 3 = 0.4771. = 3(0.3010) + 0.4771 - 2 = 0.9030 + 0.4771 - 2 = 1.3801 - 2 = -0.6199 The value of _10 0.24 is: -0.6199 Send me the next one 📸