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 ni utatuzi wa swali lako: Swali ni: _8(_3 a) + _8(_3 a) + _8(_3 a) = 1 Step 1: Unganisha maneno yanayofanana ya logariti. Kuna maneno matatu yanayofanana, hivyo tunaweza kuyaunganisha kwa kuzidisha. 3 _8(_3 a) = 1 Step 2: Gawanya pande zote mbili kwa 3 ili kutenga logariti. _8(_3 a) = (1)/(3) Step 3: Badilisha fomu ya logariti kuwa fomu ya eksponenti. Tunajua kwamba ikiwa _b x = y, basi b^y = x. Hapa, b=8, y=(1)/(3), na x=_3 a. _3 a = 8^(1)/(3) Step 4: Rahisisha upande wa kulia. 8^(1)/(3) ni sawa na mzizi wa tatu wa 8. _3 a = [3]8 _3 a = 2 Step 5: Badilisha fomu hii mpya ya logariti kuwa fomu ya eksponenti. Hapa, b=3, y=2, na x=a. a = 3^2 Step 6: Kokotoa thamani ya a. a = 9 Jibu la mwisho ni: a = 9 Tuma swali linalofuata 📸