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.
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Haya hapa ni masuluhisho ya maswali yako: 15) Tatua kwa x 1. _3 x = 4 Step 1: Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo. x = 3^4 Step 2: Kokotoa thamani. x = 3 × 3 × 3 × 3 = 81 x = 81 2. x = 2.6532 Step 1: Badilisha mlinganyo wa logariti (kwa base 10) kuwa mlinganyo wa kielelezo. x = 10^2.6532 Step 2: Kokotoa thamani. x ≈ 450.00 x ≈ 450.00 3. _2 (x+1) = 5 Step 1: Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo. x+1 = 2^5 Step 2: Kokotoa 2^5. x+1 = 32 Step 3: Tatua kwa x. x = 32 - 1 x = 31 x = 31 4. 2 x = 25 Step 1: Tumia kanuni ya logariti n a = a^n. x^2 = 25 Step 2: Ikiwa A = B, basi A = B. x^2 = 25 Step 3: Tatua kwa x. Kumbuka kuwa x lazima iwe chanya kwa sababu ya logariti. x = sqrt(25) x = 5 x = 5 STRAND 3: ALGEBRA - EXPANSIONS, FACTORISATION AND QUADRARICS Panua na Rahisisha: 3(2x-5) + 4(x+2) Step 1: Panua vigawo vilivyo nje ya mabano. 3(2x-5) = 6x - 15 4(x+2) = 4x + 8 Mlinganyo unakuwa: 6x - 15 + 4x + 8 Step 2: Unganisha vigezo vinavyofanana. (6x + 4x) + (-15 + 8) 10x - 7 Jibu ni 10x - 7 16) Tumia utambulisho wa quadratic kutathmini kikamilifu: 102^2 Step 1: Andika 102 kama jumla ya namba mbili. 102 = 100 + 2 Step 2: Tumia utambulisho wa quadratic (a+b)^2 = a^2 + 2ab + b^2. Hapa, a=100 na b=2. (100+2)^2 = 100^2 + 2(100)(2) + 2^2 Step 3: Kokotoa kila neno. 100^2 = 10000 2(100)(2) = 400 2^2 = 4 Step 4: Jumlisha matokeo. 10000 + 400 + 4 = 10404 Jibu ni 10404 Tuma swali linalofuata 📸