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É dada a função
Calculemos o logaritmo de
![\mathrm{\ell og}\big[f(x)\big]\\\\ =\mathrm{\ell og}\left(x^{\frac{2}{\mathrm{\ell og\,}x}} \right )\\\\\\ =\dfrac{2}{\mathrm{\ell og\,}x}\cdot \mathrm{\ell og}\,x\\\\\\=2~~~~~~\text{para todo }x \in(0,\,1)\cup(1,\,\infty)](https://tex.z-dn.net/?f=%5Cmathrm%7B%5Cell+og%7D%5Cbig%5Bf%28x%29%5Cbig%5D%5C%5C%5C%5C+%3D%5Cmathrm%7B%5Cell+og%7D%5Cleft%28x%5E%7B%5Cfrac%7B2%7D%7B%5Cmathrm%7B%5Cell+og%5C%2C%7Dx%7D%7D+%5Cright+%29%5C%5C%5C%5C%5C%5C+%3D%5Cdfrac%7B2%7D%7B%5Cmathrm%7B%5Cell+og%5C%2C%7Dx%7D%5Ccdot+%5Cmathrm%7B%5Cell+og%7D%5C%2Cx%5C%5C%5C%5C%5C%5C%3D2%7E%7E%7E%7E%7E%7E%5Ctext%7Bpara+todo+%7Dx+%5Cin%280%2C%5C%2C1%29%5Ccup%281%2C%5C%2C%5Cinfty%29 "\mathrm{\ell og}\big[f(x)\big]\\\\ =\mathrm{\ell og}\left(x^{\frac{2}{\mathrm{\ell og\,}x}} \right )\\\\\\ =\dfrac{2}{\mathrm{\ell og\,}x}\cdot \mathrm{\ell og}\,x\\\\\\=2~~~~~~\text{para todo }x \in(0,\,1)\cup(1,\,\infty)")
Como o logaritmo de
é constante igual a 2, vale que
![\mathrm{\ell og}\Big[f(\sqrt{3})\Big]=2](https://tex.z-dn.net/?f=%5Cmathrm%7B%5Cell+og%7D%5CBig%5Bf%28%5Csqrt%7B3%7D%29%5CBig%5D%3D2 "\mathrm{\ell og}\Big[f(\sqrt{3})\Big]=2")
Resposta: alternativa
Calculemos o logaritmo de
Como o logaritmo de
Resposta: alternativa
marimaias:
Excelente ,me ajudou mt!!
Por nada! :-)
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