Question

Arrange the following in ascending order:
${\log }_{3}108,{\log }_{4}192,{\log }_{5}500,{\log }_{6}1080$

• A. ${\log }_{3}108<{\log }_{4}192<{\log }_{5}500<{\log }_{6}1080$
  
• B. ${\log }_{4}192>{\log }_{5}500<{\log }_{6}1080<{\log }_{3}108$
• C. ${\log }_{4}192<{\log }_{5}500>{\log }_{6}1080<{\log }_{3}108$
• D. None of these

Answer 1

Answer: (A)

${\log }_{3}108<{\log }_{4}192<{\log }_{5}500<{\log }_{6}1080$

$lo{g}_{3}108=\frac{log108}{log3}=4.26$

$lo{g}_{4}192=\frac{log192}{log4}=3.792$

$lo{g}_{5}500=\frac{log500}{log5}=3.861$

$lo{g}_{6}1080=\frac{log1080}{log6}=3.8982$

Arranging them in ascending order we get

$lo{g}_{4}192,lo{g}_{5}500.lo{g}_{6}1080,lo{g}_{3}108$