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
here's the solution for question 1b: Step 1: Simplify the left side of the equation. The given equation is (3)/(2) × (16)/(4) = 10^c. First, simplify the multiplication on the left side: (3)/(2) × (16)/(4) = (3 × 16)/(2 × 4) (3 × 16)/(2 × 4) = (48)/(8) (48)/(8) = 6 Step 2: Set the simplified value equal to the right side of the equation. Now the equation becomes: 6 = 10^c Step 3: Solve for c using logarithms. To find the value of c, take the common logarithm (base 10) of both sides of the equation: _10(6) = _10(10^c) Using the logarithm property _b(b^x) = x: _10(6) = c We can calculate _10(6) using the values from the previous problem, where 2 = 0.3010 and 3 = 0.4771: _10(6) = _10(2 × 3) _10(6) = _10(2) + _10(3) _10(6) = 0.3010 + 0.4771 _10(6) = 0.7781 Therefore, c = 0.7781. The final answer is c=0.7781. Drop the next question!