log(x-1)+log(x+1) = log8+log(x-2)
f
istnieja 2 pierwiastki:
x=<3,5>
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f![obliczamy\ dziedzine\\ x-1>0 \\x>1\\ x+1>0\\ x>-1 \\x-2>0\\x>2\\ D=(-\infty,8> \ v <-1,1>\ v <2,\infty) \\log(x-1)+log(x+1)=log8+log(x-2)\\log[(x-1)*(x+1)]=log[8*(x-2)]\\log(x^{2}-1)=log(8x-16)\\x^{2}-1=8x-16\\ x^{2}-8x+15=0\\delta=64-4*1*15\\delta=64-60=4\\\sqrt{delta}=2 obliczamy\ dziedzine\\ x-1>0 \\x>1\\ x+1>0\\ x>-1 \\x-2>0\\x>2\\ D=(-\infty,8> \ v <-1,1>\ v <2,\infty) \\log(x-1)+log(x+1)=log8+log(x-2)\\log[(x-1)*(x+1)]=log[8*(x-2)]\\log(x^{2}-1)=log(8x-16)\\x^{2}-1=8x-16\\ x^{2}-8x+15=0\\delta=64-4*1*15\\delta=64-60=4\\\sqrt{delta}=2](https://tex.z-dn.net/?f=obliczamy%5C+dziedzine%5C%5C+x-1%3E0+%5C%5Cx%3E1%5C%5C+x%2B1%3E0%5C%5C+x%3E-1+%5C%5Cx-2%3E0%5C%5Cx%3E2%5C%5C+D%3D%28-%5Cinfty%2C8%3E+%5C+v+%3C-1%2C1%3E%5C+v+%3C2%2C%5Cinfty%29+%5C%5Clog%28x-1%29%2Blog%28x%2B1%29%3Dlog8%2Blog%28x-2%29%5C%5Clog%5B%28x-1%29%2A%28x%2B1%29%5D%3Dlog%5B8%2A%28x-2%29%5D%5C%5Clog%28x%5E%7B2%7D-1%29%3Dlog%288x-16%29%5C%5Cx%5E%7B2%7D-1%3D8x-16%5C%5C+x%5E%7B2%7D-8x%2B15%3D0%5C%5Cdelta%3D64-4%2A1%2A15%5C%5Cdelta%3D64-60%3D4%5C%5C%5Csqrt%7Bdelta%7D%3D2)
istnieja 2 pierwiastki:
x=<3,5>