Answer:
![\large\boxed{x=\dfrac{-3+\sqrt{40+10\sqrt{10}}}{2}}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Bx%3D%5Cdfrac%7B-3%2B%5Csqrt%7B40%2B10%5Csqrt%7B10%7D%7D%7D%7B2%7D%7D)
Step-by-step explanation:
![2\log x=3-2\log(x+3)\\\\Domain:\ x>0\ \wedge\ x+3>0\to x>-3\\\\D:x>0\\============================\\2\log x=3-2\log(x+3)\qquad\text{add}\ 2\log(x+3)\ \text{to both sides}\\\\2\log x+2\log(x+3)=3\qquad\text{divide both sides by 2}\\\\\log x+\log(x+3)=\dfrac{3}{2}\qquad\text{use}\ \log_ab+\log_ac=\log_a(bc)\\\\\log\bigg(x(x+3)\bigg)=\dfrac{3}{2}\qquad\text{use the de}\text{finition of a logarithm}\\\\x(x+3)=10^\frac{3}{2}\qquad\text{use the distributive property}](https://tex.z-dn.net/?f=2%5Clog%20x%3D3-2%5Clog%28x%2B3%29%5C%5C%5C%5CDomain%3A%5C%20x%3E0%5C%20%5Cwedge%5C%20x%2B3%3E0%5Cto%20x%3E-3%5C%5C%5C%5CD%3Ax%3E0%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C2%5Clog%20x%3D3-2%5Clog%28x%2B3%29%5Cqquad%5Ctext%7Badd%7D%5C%202%5Clog%28x%2B3%29%5C%20%5Ctext%7Bto%20both%20sides%7D%5C%5C%5C%5C2%5Clog%20x%2B2%5Clog%28x%2B3%29%3D3%5Cqquad%5Ctext%7Bdivide%20both%20sides%20by%202%7D%5C%5C%5C%5C%5Clog%20x%2B%5Clog%28x%2B3%29%3D%5Cdfrac%7B3%7D%7B2%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%5Clog_ab%2B%5Clog_ac%3D%5Clog_a%28bc%29%5C%5C%5C%5C%5Clog%5Cbigg%28x%28x%2B3%29%5Cbigg%29%3D%5Cdfrac%7B3%7D%7B2%7D%5Cqquad%5Ctext%7Buse%20the%20de%7D%5Ctext%7Bfinition%20of%20a%20logarithm%7D%5C%5C%5C%5Cx%28x%2B3%29%3D10%5E%5Cfrac%7B3%7D%7B2%7D%5Cqquad%5Ctext%7Buse%20the%20distributive%20property%7D)
![x^2+3x=10^{1\frac{1}{2}}\\\\x^2+3x=10^{1+\frac{1}{2}}\qquad\text{use}\ a^n\cdot a^m=a^{n+m}\\\\x^2+3x=10\cdot10^\frac{1}{2}\qquad\text{use}\ \sqrt[n]{a}=a^\frac{1}{n}\\\\x^2+3x=10\sqrt{10}\qquad\text{subtract}\ 10\sqrt{10}\ \text{from both sides}\\\\x^2+3x-10\sqrt{10}=0\\\\\text{Use the quadratic formula}\\\\ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\a=1,\ b=3,\ c=-10\sqrt{10}\\\\b^2-4ac=3^2-4(1)(-10\sqrt{10})=9+40\sqrt{10}\\\\x=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2(1)}=\dfrac{-3\pm\sqrt{40+10\sqrt{10}}}{2}\\\\x=\dfrac{-3-\sqrt{10+10\sqrt{10}}}{2}\notin D](https://tex.z-dn.net/?f=x%5E2%2B3x%3D10%5E%7B1%5Cfrac%7B1%7D%7B2%7D%7D%5C%5C%5C%5Cx%5E2%2B3x%3D10%5E%7B1%2B%5Cfrac%7B1%7D%7B2%7D%7D%5Cqquad%5Ctext%7Buse%7D%5C%20a%5En%5Ccdot%20a%5Em%3Da%5E%7Bn%2Bm%7D%5C%5C%5C%5Cx%5E2%2B3x%3D10%5Ccdot10%5E%5Cfrac%7B1%7D%7B2%7D%5Cqquad%5Ctext%7Buse%7D%5C%20%5Csqrt%5Bn%5D%7Ba%7D%3Da%5E%5Cfrac%7B1%7D%7Bn%7D%5C%5C%5C%5Cx%5E2%2B3x%3D10%5Csqrt%7B10%7D%5Cqquad%5Ctext%7Bsubtract%7D%5C%2010%5Csqrt%7B10%7D%5C%20%5Ctext%7Bfrom%20both%20sides%7D%5C%5C%5C%5Cx%5E2%2B3x-10%5Csqrt%7B10%7D%3D0%5C%5C%5C%5C%5Ctext%7BUse%20the%20quadratic%20formula%7D%5C%5C%5C%5Cax%5E2%2Bbx%2Bc%3D0%5C%5C%5C%5Cx%3D%5Cdfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%5C%5C%5C%5Ca%3D1%2C%5C%20b%3D3%2C%5C%20c%3D-10%5Csqrt%7B10%7D%5C%5C%5C%5Cb%5E2-4ac%3D3%5E2-4%281%29%28-10%5Csqrt%7B10%7D%29%3D9%2B40%5Csqrt%7B10%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-3%5Cpm%5Csqrt%7B40%2B10%5Csqrt%7B10%7D%7D%7D%7B2%281%29%7D%3D%5Cdfrac%7B-3%5Cpm%5Csqrt%7B40%2B10%5Csqrt%7B10%7D%7D%7D%7B2%7D%5C%5C%5C%5Cx%3D%5Cdfrac%7B-3-%5Csqrt%7B10%2B10%5Csqrt%7B10%7D%7D%7D%7B2%7D%5Cnotin%20D)
Answer:
(0,9) (-1,0), (2,0), (3,0),
Step-by-step explanation:
add me on discord LD BrxzyYT#8144 :)
1:15 pm + 5 minutes =1:20 PM You add 5 minutes because your watch is slow then subtract 3 minutes because you thought the watch was 3 minutes fast. real time is 1:17 PM
1:20 pm - 3 minutes = 1:17 PM