Question

jee mains class 11 question​

Answer 1

Step-by-step explanation:

We have,

$\log_{ \frac{1}{2} } [ \log_{ \sqrt{5}} \{ \log_{3}(243) \}]$

$= \log_{ \frac{1}{2} } [ \log_{ \sqrt{5}} \{ \log_{3}(3) ^{5} \}]$

$= \log_{ \frac{1}{2} } [ \log_{ \sqrt{5}} \{ 5\log_{3}(3) \}]$

$= \log_{ \frac{1}{2} } [ \log_{ \sqrt{5}} \{ 5 \}]$

$= \log_{ \frac{1}{2} } [ \log_{ \sqrt{5}} \{ \sqrt{5} \} ^{2} ]$

$= \log_{ \frac{1}{2} } [2 \log_{ \sqrt{5}} ( \sqrt{5} )]$

$= \log_{ \frac{1}{2} } [2 ]$

$= \log_{ \frac{1}{2} } \bigg( \frac{1}{2} \bigg)^{ - 1}$

$= - 1\log_{ \frac{1}{2} } \bigg( \frac{1}{2} \bigg)$

$= - 1$