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 33: Tunapewa mlinganyo: _2 (x+1) - _2 (x-1) = 3 Hatua ya 1: Tumia sheria ya logariti _b A - _b B = _b ((A)/(B)). _2 ((x+1)/(x-1)) = 3 Hatua ya 2: Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo (exponential equation). Kumbuka kwamba _b y = x ni sawa na b^x = y. Hivyo, 2^3 = (x+1)/(x-1) Hatua ya 3: Rahisisha na tatua kwa x. 8 = (x+1)/(x-1) Zidisha pande zote mbili kwa (x-1): 8(x-1) = x+1 8x - 8 = x+1 Toa x kutoka pande zote mbili: 7x - 8 = 1 Ongeza 8 pande zote mbili: 7x = 9 Gawanya kwa 7: x = (9)/(7) Hatua ya 4: Hakikisha thamani ya x inafanya hoja za logariti kuwa chanya. Kwa x = (9)/(7): x+1 = (9)/(7) + 1 = (9+7)/(7) = (16)/(7) > 0 x-1 = (9)/(7) - 1 = (9-7)/(7) = (2)/(7) > 0 Thamani ya x ni halali. x = (9)/(7) That's 2 down. 3 left today — send the next one.