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 utatuzi wa swali la 35: Tunapewa mlinganyo: 32^(x-3) ÷ 8^(x+4) = 64 ÷ 2^x Hatua ya 1: Andika nambari zote kama nguvu za 2. Tunajua kuwa 32 = 2^5, 8 = 2^3, na 64 = 2^6. Badilisha nambari hizi kwenye mlinganyo: (2^5)^(x-3) ÷ (2^3)^(x+4) = 2^6 ÷ 2^x Hatua ya 2: Tumia sheria ya viashiria (a^m)^n = a^mn. 2^5(x-3) ÷ 2^3(x+4) = 2^6 ÷ 2^x 2^(5x-15) ÷ 2^(3x+12) = 2^6 ÷ 2^x Hatua ya 3: Tumia sheria ya viashiria a^m ÷ a^n = a^m-n. 2^(5x-15) - (3x+12) = 2^(6-x) 2^(5x-15-3x-12) = 2^(6-x) 2^(2x-27) = 2^(6-x) Hatua ya 4: Kwa kuwa besi (base) ni sawa, linganisha viashiria (exponents). 2x - 27 = 6 - x Hatua ya 5: Tatua kwa x. Ongeza x pande zote mbili: 2x + x - 27 = 6 3x - 27 = 6 Ongeza 27 pande zote mbili: 3x = 6 + 27 3x = 33 Gawanya kwa 3: x = (33)/(3) x = 11 Tuma swali linalofuata 📸