0\ \wedge\ 3x-5 > 0\\\\x > \frac{1}{3}\ \wedge\ x > \frac{5}{3}\\\\x\in\left(\frac{5}{3};\ \infty\right)" alt="log_3(3x-1)+log_3(3x-5)=1\\\\D:3x-1 > 0\ \wedge\ 3x-5 > 0\\\\x > \frac{1}{3}\ \wedge\ x > \frac{5}{3}\\\\x\in\left(\frac{5}{3};\ \infty\right)" align="absmiddle" class="latex-formula">
![log_3\left[(3x-1)(3x-5)\right]=log_33\iff(3x-1)(3x-5)=3\\\\9x^2-15x-3x+5-3=0\\\\9x^2-18x+2=0\\\\\Delta=(-18)^2-4\cdot9\cdot2=324-72=252\\\\\sqrt\Delta=\sqrt{252}=\sqrt{36\cdot7}=6\sqrt7\\\\x_1=\frac{18-6\sqrt7}{2\cdot9}=\frac{3-\sqrt7}{3}\notin D;\ x_2=\frac{18+6\sqrt7}{2\cdot9}=\frac{3+\sqrt7}{3}\in D](https://tex.z-dn.net/?f=log_3%5Cleft%5B%283x-1%29%283x-5%29%5Cright%5D%3Dlog_33%5Ciff%283x-1%29%283x-5%29%3D3%5C%5C%5C%5C9x%5E2-15x-3x%2B5-3%3D0%5C%5C%5C%5C9x%5E2-18x%2B2%3D0%5C%5C%5C%5C%5CDelta%3D%28-18%29%5E2-4%5Ccdot9%5Ccdot2%3D324-72%3D252%5C%5C%5C%5C%5Csqrt%5CDelta%3D%5Csqrt%7B252%7D%3D%5Csqrt%7B36%5Ccdot7%7D%3D6%5Csqrt7%5C%5C%5C%5Cx_1%3D%5Cfrac%7B18-6%5Csqrt7%7D%7B2%5Ccdot9%7D%3D%5Cfrac%7B3-%5Csqrt7%7D%7B3%7D%5Cnotin+D%3B%5C+x_2%3D%5Cfrac%7B18%2B6%5Csqrt7%7D%7B2%5Ccdot9%7D%3D%5Cfrac%7B3%2B%5Csqrt7%7D%7B3%7D%5Cin+D "log_3\left[(3x-1)(3x-5)\right]=log_33\iff(3x-1)(3x-5)=3\\\\9x^2-15x-3x+5-3=0\\\\9x^2-18x+2=0\\\\\Delta=(-18)^2-4\cdot9\cdot2=324-72=252\\\\\sqrt\Delta=\sqrt{252}=\sqrt{36\cdot7}=6\sqrt7\\\\x_1=\frac{18-6\sqrt7}{2\cdot9}=\frac{3-\sqrt7}{3}\notin D;\ x_2=\frac{18+6\sqrt7}{2\cdot9}=\frac{3+\sqrt7}{3}\in D")