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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Hili hapa suluhisho la mlinganyo: Tunapewa mlinganyo: 5^2x + 5^2x+1 = 100 Step 1: Tumia sheria ya vipeo a^m+n = a^m · a^n kurahisisha 5^2x+1. 5^2x + 5^2x · 5^1 = 100 Step 2: Toa 5^2x kama kigezo cha kawaida. 5^2x(1 + 5) = 100 Step 3: Rahisisha usemi ndani ya mabano. 5^2x(6) = 100 Step 4: Gawanya pande zote mbili kwa 6 ili kutenga 5^2x. 5^2x = (100)/(6) 5^2x = (50)/(3) Step 5: Ili kutatua x, tunahitaji kutumia logariti. Chukua logariti ya msingi 5 pande zote mbili. _5(5^2x) = _5((50)/(3)) Step 6: Tumia sheria ya logariti _b(b^y) = y na _b((M)/(N)) = _b M - _b N. 2x = _5(50) - _5(3) 2x = _5(25 · 2) - _5(3) 2x = _5(25) + _5(2) - _5(3) 2x = _5(5^2) + _5(2) - _5(3) 2x = 2 + _5(2) - _5(3) Step 7: Gawanya pande zote mbili kwa 2 ili kupata x. x = (2 + _5(2) - _5(3))/(2) x = 1 + (_5(2) - _5(3))/(2) Kama unahitaji jibu la nambari, tunaweza kukadiria maadili ya logariti: _5(2) ≈ 0.430676 _5(3) ≈ 0.682606 x ≈ 1 + (0.430676 - 0.682606)/(2) x ≈ 1 + (-0.25193)/(2) x ≈ 1 - 0.125965 x ≈ 0.874035 Jibu la mwisho ni: x = 1 + (_5(2) - _5(3))/(2) Tuma swali linalofuata 📸