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
Hapa kuna hatua za kutatua mlinganyo wa logariti: Mlinganyo uliotolewa ni: _2 (5x - 3) - 2 = _2 (x + 1) Step 1: Panga upya mlinganyo ili kuweka maneno ya logariti upande mmoja. _2 (5x - 3) - _2 (x + 1) = 2 Step 2: Badilisha namba 2 kuwa logariti yenye base 2. Tunajua kuwa 2 = _2 (2^2) = _2 4. _2 (5x - 3) - _2 (x + 1) = _2 4 Step 3: Tumia sheria ya logariti _b A - _b B = _b ((A)/(B)) kuunganisha maneno ya logariti upande wa kushoto. _2 ((5x - 3)/(x + 1)) = _2 4 Step 4: Kwa kuwa base za logariti ni sawa, tunaweza kulinganisha hoja (arguments) zao. (5x - 3)/(x + 1) = 4 Step 5: Tatua mlinganyo kwa x. Anza kwa kuzidisha pande zote mbili kwa (x + 1). 5x - 3 = 4(x + 1) 5x - 3 = 4x + 4 Toa 4x kutoka pande zote mbili: x - 3 = 4 Ongeza 3 kwa pande zote mbili: x = 7 Step 6: Hakikisha suluhisho ni halali kwa kuangalia masharti ya logariti (hoja lazima ziwe chanya). Kwa 5x - 3: 5(7) - 3 = 35 - 3 = 32 > 0 (Halali) Kwa x + 1: 7 + 1 = 8 > 0 (Halali) Kwa kuwa masharti yote yametimizwa, x = 7 ni suluhisho sahihi. Jibu la mwisho ni: x = 7 Tuma swali linalofuata 📸