Question

Sort the following in increasing order.

• A. ${\log }_2\left(8\right)$
• B. ${\log }_3\left(81\right)$
• C. ${\log }_{10}\left(100000\right)$
• D. ${\log }_2\left(64\right)$

Answer 1

${\log }_m{m}^n=nlo{g}_{m}m$
${\log }_{2}8$ = ${\log }_2{2}^3$ = 3
${\log }_{3}81$ = ${\log }_3{3}^4$ = 4
${\log }_{10}100000$ = ${\log }_{10}{10}^5$ = 5
${\log }_{2}64$ = ${\log }_2{2}^6$ = 6
3<4<5<6
$\therefore$ ${\log }_{2}8$ < ${\log }_{3}81$ < ${\log }_{10}100000$ < ${\log }_{2}64$