# How do you write Log_2 1024 = 10  in exponential form?

Aug 31, 2016

${2}^{10} = 1024$

#### Explanation:

${\log}_{a} b = n$ in exponential form is written as ${a}^{n} = b$.

Hence, ${\log}_{2} 1024 = 10$ can be written in exponential form as

${2}^{10} = 1024$

Aug 31, 2016

${2}^{10} = 1024$

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

#### Explanation:

log form and exponential (or index) form are interchangeable.

Simply remember:

"The base stays the base, and the other two swop around"

${\log}_{\textcolor{red}{a}} \textcolor{b l u e}{b} = \textcolor{\lim e}{c} \Leftrightarrow {\textcolor{red}{a}}^{\textcolor{\lim e}{c}} = \textcolor{b l u e}{b}$

What is ${\log}_{2} 1024$ ?

In log form the question being asked is ...

"What index/power of 2 will give 1024?"

It is a real advantage to know all the powers up to 1000.

${2}^{10} = 1024$

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