Question

Write $2^{10}=1024$ in logarithmic form.

Answer 1

$2^{10}=1024$

Applying $\log$ both sides, we get

${\log }_2{2}^{10}={\log }_{2}1024$

$\Rightarrow 10{\log }_{2}2={\log }_{2}1024$

using $\log a^m=m\log a$

$\Rightarrow 10={\log }_{2}1024$ using ${\log }_{a}a=1$

$\therefore {\log }_{2}1024=10$