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
Alright Olamide — let's do this. Step 1: Apply the power rule of logarithms, c _b(a) = _b(a^c), to the second term. 2_10((5)/(9)) = _10(((5)/(9))^2) = _10((25)/(81)) The original expression now becomes: _10((30)/(16)) - _10((25)/(81)) + _10((48)/(243)) Step 2: Combine the logarithmic terms using the quotient rule, _b(x) - _b(y) = _b((x)/(y)), and the product rule, _b(x) + _b(y) = _b(xy). _10((30)/(16)(25)/(81) × (48)/(243)) This simplifies to: _10((30)/(16) × (81)/(25) × (48)/(243)) Step 3: Simplify the fraction inside the logarithm. First, simplify each individual fraction: (30)/(16) = (15)/(8) (48)/(243) = (16 × 3)/(81 × 3) = (16)/(81) Substitute these simplified fractions back into the expression: _10((15)/(8) × (81)/(25) × (16)/(81)) Cancel out common factors (81 in the numerator and denominator, and 8 with 16): _10((15)/(1) × (1)/(25) × (2)/(1)) Multiply the remaining terms: _10((15 × 2)/(25)) Simplify further by dividing 15 and 25 by 5: _10((3 × 2)/(5)) _10((6)/(5)) The simplified expression is: _10((6)/(5)) What's next? Send 'em! 📸