Question

${\log }_{2}8=3$ means ${\log }_{8}2=\frac{1}{a}$
then $a$=

Answer 1

${\log }_{2}8=\frac{\log 8}{\log 2}$ ...(since ${\log }_{b}a=\frac{\log a}{\log b}$)

$\therefore \frac{\log 2^3}{\log 2}=3$ ...($\log a^b=b\log a$)

${\log }_{8}2=\frac{\log 2}{\log 8}$ ...(since ${\log }_{b}a=\frac{\log a}{\log b}$)

$\therefore \frac{\log 2}{\log 2^3}=\frac{1}{3}$ ...($\log a^b=b\log a$)

$a=3$