Question 1

1)    $\log _{\frac{1}{e}}e\leq \log _{\frac{1}{e}}x$

Accepted Answer

$x\leq e$

Answer

$x\leq-e\vee x\geq e$

Answer

$x\geq e$

Answer

$-e\leq x \leq e$

Question 2

2)        $2\ln x+\ln 5\geq\ln 80$

Accepted Answer

$ x\geq4$

Answer

$x \leq 4$

Answer

$-4\leq x \leq 4$

Answer

$x\leq-4\vee x\geq4$

Question 3

3)    $\log _{\frac{1}{3}} \left(x+2 \right) +\log _{\frac{1}{3}} \left( x-2  \right) \geq \log  _{\frac{1}{3}} 21$

Accepted Answer

$2< x \leq 5$

Answer

$2> x \leq 5$

Answer

$x\leq-5\vee x\geq5$

Answer

$-5\leq x\leq5$

Question 4

4)    $\log_{3} \left( 12-x  \right) \leq3-\log_{3}x$

Accepted Answer

$0<x \leq 3$ $\vee$ $9\leq x <12$

Answer

$0<x \leq 9$

Answer

$3\leq x <12$

Answer

$0\leq x < 12$

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