First slide

Trigonometric Identities

Question

If $S = \{x \in R : (\log_{0, 6} 0 .216) \log_{5} (5 - 2 x) \leq 0\}$ then S is equal to

Moderate

A

$[2.5, \infty)$
B

$[2, 2.5)$
C

$(2, 2.5)$
D

(0,25)

Solution

$\begin{array}{l} (\log_{(0 .6)} (0 .6)^{3}) \log_{5} (5 - 2 x) \leq 0 \\ \Rightarrow 5 - 2 x \leq 1 \\ \Rightarrow x \geq 2 - - - (i) \end{array}$
Also, 5 -2x > 0 ---------(ii)
From Eqs. (i) and (ii), we have $x \in [2, 2 .5)$

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