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
Ili kutatua x, tutatumia kanuni za logariti. Step 1: Rahisisha upande wa kulia wa mlinganyo. Tunajua kuwa _b b = 1. Kwa hiyo, _2 2 = 1. _2(x^2 - 9) = 3_2 2 + 1 _2(x^2 - 9) = 3(1) + 1 _2(x^2 - 9) = 3 + 1 _2(x^2 - 9) = 4 Step 2: Badilisha mlinganyo wa logariti kuwa mlinganyo wa kielelezo. Kama _b A = C, basi b^C = A. 2^4 = x^2 - 9 Step 3: Kokotoa 2^4. 16 = x^2 - 9 Step 4: Tatua mlinganyo wa aljebra kwa x. Ongeza 9 pande zote mbili. 16 + 9 = x^2 25 = x^2 Step 5: Chukua mzizi wa mraba wa pande zote mbili. x = ±sqrt(25) x = ± 5 Step 6: Thibitisha suluhisho. Kwa logariti, hoja (x^2 - 9) lazima iwe chanya. Kwa x=5: 5^2 - 9 = 25 - 9 = 16 > 0. Hii ni halali. Kwa x=-5: (-5)^2 - 9 = 25 - 9 = 16 > 0. Hii pia ni halali. Jibu la mwisho ni: x = ± 5 That's 2 down. 3 left today — send the next one.