Ayudaaaaaaaa?

<img src="https://tex.z-dn.net/?f=%5Clog_3%20n%3D%5Clog_6m%3D%5Clog_%7B12%7D%28m%2Bn%29%3Dk%5Ctext%7B%20entonces%20por%20de%7D%20%5Ctext%7Bfinici%5C%27on%20del%20logaritmo%7D%5C%5C%5Ctext%7Btenemos%3A%7D%5C%5C%5C%5C%5Clog_3%20n%3Dk%5Cto%20n%3D3%5Ek~%5Ccdots%5Ccdots%5Ccdots%281%29%5C%5C%5Clog_6m%3Dk%5Cto%20m%3D6%5Ek~%5Ccdots%5Ccdots%5Ccdots%282%29%5C%5C%5Clog_%7B12%7D%28m%2Bn%29%3Dk%5Cto%20m%2Bn%3D12%5Ek~%5Ccdots%5Ccdots%5Ccdots%283%29%5C%5C%20%5C%5C%5Ctext%7BSumamos%20%281%29%2B%282%29%3D%283%29%3A%7D%5C%5C%5C%5C3%5Ek%2B6%5Ek%3D12%5Ek%5C%5C%20%5C%5C3%5Ek%2B%282%5Ctimes%203%29%5Ek%3D%283%5Ctimes4%29%5Ek%5C%5C%5Ctext%7BDividimos%20todo%20entre%20%7D3%5Ek%3A%5C%5C%5C%5C1%2B2%5Ek%3D4%5Ek%5C%5C1%2B2%5Ek%3D%282%5E2%29%5Ek%5C%5C1%2B2%5Ek%3D%282%5Ek%29%5E2%5C%5C%282%5Ek%29%5E2-2%5E%7Bk%7D-1%3D0%5C%5C%5Ctext%7BPor%20Baskara%3A%7D%5C%5C%20%5C%5C2%5Ek%3D%5Cdfrac%7B1%5Cpm%5Csqrt%7B1%5E2-4%281%29%28-1%29%7D%7D%7B2%7D" /><img src="https://tex.z-dn.net/?f=2%5Ek%3D%5Cdfrac%7B1%5Cpm%5Csqrt%7B5%7D%7D%7B2%7D%5C%5C%20%5C%5C%5Ctext%7BSi%20%24k%5Cin%5Cmathbb%7BR%7D%24%20entonces%20%7D2%5Ek%3E0%20%5Ctext%7B%20por%20lo%20tanto%3A%20%7D%5C%5C%5C%5C2%5Ek%3D%5Cdfrac%7B1%2B%5Csqrt%7B5%7D%7D%7B2%7D%5C%5C%20%5C%5C%5Ctext%7BLuego%3A%20%7D%5C%5C%20%5C%5C%5Cdfrac%7Bm%7D%7Bn%7D%3D%5Cdfrac%7B6%5Ek%7D%7B3%5Ek%7D%3D2%5Ek%5C%5C%20%5C%5C%5Cboxed%7B%5Cdfrac%7Bm%7D%7Bn%7D%3D%5Cdfrac%7B1%2B%5Csqrt%7B5%7D%7D%7B2%7D%7D" />0 \ text{ por lo tanto : } \ \ \ \ 2 ^ k = \ dfrac{1 + \ sqrt{5}}{2} \ \ \ \ \ text{Luego : } \ \ \ \ \ dfrac{m}{n} = \ dfrac{6 ^ k}{3 ^ k} = 2 ^ k \ \ \ \ \ boxed{ \ dfrac{m}{n} = \ dfrac{1 + \ sqrt{5}}{2}}" alt = "2 ^ k = \ dfrac{1 \ pm \ sqrt{5}}{2} \ \ \ \ \ text{Si $k \ in \ mathbb{R}$ entonces }2 ^ k>0 \ text{ por lo tanto : } \ \ \ \ 2 ^ k = \ dfrac{1 + \ sqrt{5}}{2} \ \ \ \ \ text{Luego : } \ \ \ \ \ dfrac{m}{n} = \ dfrac{6 ^ k}{3 ^ k} = 2 ^ k \ \ \ \ \ boxed{ \ dfrac{m}{n} = \ dfrac{1 + \ sqrt{5}}{2}}" align = "absmiddle" class = "latex - formula">.