Exercício sobre equação exponencial e logarítmica

Resolver:

$\phantom{X}3^{{}^{\LARGE x}}\,=\,243\phantom{XXXXXX}$

$\phantom{X}3^{{}^{\LARGE x}}\,\gt\,243\phantom{X}$

$\phantom{X}3^{{}^{\LARGE x}}\,\lt\,243\phantom{X}$

$\phantom{X}(\dfrac{1}{2})^{{}^{\LARGE x}}\,=\,\dfrac{1}{16}\phantom{X}$

$\phantom{X}(\dfrac{1}{2})^{{}^{\LARGE x}}\,\gt\,\dfrac{1}{16}\phantom{X}$

$\phantom{X}(\dfrac{1}{2})^{{}^{\LARGE x}}\,\lt\,\dfrac{1}{16}\phantom{X}$

$\phantom{X}log{{}_{\Large 2\,}}x\,=\,log{{}_{\Large 2\,}}7\phantom{X}$

$\phantom{X}log{{}_{\Large 2\,}}x\,\gt\,log{{}_{\Large 2\,}}7\phantom{X}$

$\phantom{X}log{{}_{\Large 2\,}}x\,\lt\,log{{}_{\Large 2\,}}7\phantom{X}$

$\phantom{X}log{{}_{\Large \frac{1}{3}\,}}x\,=\,log{{}_{\Large \frac{1}{3}\,}}4\phantom{X}$

$\phantom{X}log{{}_{\Large \frac{1}{3}\,}}x\,\gt\,log{{}_{\Large \frac{1}{3}\,}}4\phantom{X}$

$\phantom{X}log{{}_{\Large \frac{1}{3}\,}}x\,\lt\,log{{}_{\Large \frac{1}{3}\,}}4\phantom{X}$

$\phantom{X}log{{}_{\Large 3\,}}(x\,-\,2)\,=\,4\phantom{X}$

$\phantom{X}log{{}_{\Large \frac{1}{2}\,}}(x\,-\,7)\,\lt\,2\phantom{X}$

$\phantom{X}log{{}_{\Large 3\,}}(x\,-\,1)\,\gt\,0\phantom{X}$

$\phantom{X}log{{}_{\Large 5\,}}(x\,-\,2)\,\lt\,0\phantom{X}$

resposta: a) 5 b) x > 5 c) x < 5 d) x = 4 e) x < 4 f) x > 4 g) x = 7 h) x > 7 i) 0 < x < 7 j) x = 4 k) 0 < x < 4 l) x > 4 m) x = 83 n) x > 29/4 o) x > 2 p) 2 < x < 3
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