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GrogVix [38]
2 years ago
10

If

rm log_{3}( |5 - 2x| ) > 4" alt=" \rm log_{3}( |5 - 2x| ) > 4" align="absmiddle" class="latex-formula"> then x lies in interval of :
i)
( - 43 \: , \: 38)
ii)
( -  \infty  \: , \: 38 ) \cup(43 \: , \:  \infty )
iii)
( - 38 \: , \: 43)
iv)
( -  \infty  \: , \:  - 43) \cup(38 \: , \:  \infty )
​

Mathematics
1 answer:
Greeley [361]2 years ago
7 0

\log_3|5-2x| > 4\\\log_3|5-2x| > \log_33^4\\|5-2x| > 3^4\\|5-2x| > 81\\5-2x > 81 \vee 5-2x < -81\\2x < -76 \vee 2x > 86\\x < -38 \vee x > 43\\x\in(-\infty,-38)\cup(43,\infty)

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