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
Huu hapa ni utatuzi wa swali lako: 2. Eleza _10 63_10 147 kwa kutumia x na y. Step 1: Andika nambari 63 na 147 kama bidhaa za vigawo vikuu. 63 = 9 × 7 = 3^2 × 7 147 = 3 × 49 = 3 × 7^2 Step 2: Rahisisha _10 63 kwa kutumia sheria za logariti. Tunajua _10 3 = x na _10 7 = y. _10 63 = _10 (3^2 × 7) Tumia sheria ya kuzidisha ya logariti (_b (MN) = _b M + _b N): _10 (3^2 × 7) = _10 (3^2) + _10 7 Tumia sheria ya nguvu ya logariti (_b (M^p) = p _b M): _10 (3^2) + _10 7 = 2 _10 3 + _10 7 Badilisha x na y: 2x + y Step 3: Rahisisha _10 147 kwa kutumia sheria za logariti. _10 147 = _10 (3 × 7^2) Tumia sheria ya kuzidisha ya logariti: _10 (3 × 7^2) = _10 3 + _10 (7^2) Tumia sheria ya nguvu ya logariti: _10 3 + _10 (7^2) = _10 3 + 2 _10 7 Badilisha x na y: x + 2y Step 4: Andika usemi wa mwisho. Sasa tunaweza kuandika usemi wa asili kwa kutumia x na y: _10 63_10 147 = (2x + y)/(x + 2y) Usemi katika x na y ni (2x + y)/(x + 2y). 3 done, 2 left today. You're making progress.