Exercício sobre função logaritmica

Resolver a inequação $\phantom{X}log_{{}_{\Large 2}}({2^{{}^{\LARGE x\,+\,1}}\,-\,2)}\;\lt\;x\phantom{X}$

resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,\mathbb{R}\,|\,0\,\lt\,x\,\lt\,1\rbrace\,$
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Resolver a inequação $\phantom{X}log_{{}_{\LARGE(x\,-\,3)}}{\pi}\;\gt\;log_{{}_{\LARGE(x\,-\,3)}}4\phantom{X}$

resposta: $\,\mathbb{S}\,=\,\lbrace x\,\in\,\mathbb{R}\,|\,3\,\lt\,x\,\lt\,4\rbrace\,$
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Resolver a inequação $\phantom{X}log_{{}_{\LARGE \,(x^2\,-\,4)}}4\;\lt\;log_{{}_{\LARGE \,(x^2\,-\,4)}}5\phantom{X}$

resposta: $\,\mathbb{V}\,=\,\lbrace x\,\in\,\mathbb{R}\,|\,x\,\lt\,-\sqrt{5}\;{\text ou}\; \sqrt{5}\,\lt\,x\rbrace\,$
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Resolver a inequação $\phantom{X}log{{}_{\Large 7\,}}x\;\geqslant\;log_{{}_{\Large 7\,}}3\;+\;\dfrac{1}{\;2\;}log{{}_{\Large 7\,}}(x\,-\,2)\phantom{X}$

resposta: $\,S\,=\,\lbrace\,x\,\in\,\mathbb{R}\;|\;2\,\lt\,x\,\leqslant\,3\;{\text ou}\;x\,\geqslant\,6\rbrace\,$
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