logarithm base 2

ender · **Joined:** Thu, 22 Jun 2006 01:08:00 UTC **Posts:** 123

hi, any hint will be appreciated:

obtain

from
$n^{3/2}\leq e^{k}$

but i need to express this in terms of logarithms with base 2 because is for applications into computer stuff.
i know that the answer would be

$\ln {n^{3/2}}=k$

but as i said, nedd some way to put this in terms of logarithms base 2. any idea?

thanks!

Shadow · **Posted:** Tue, 26 Jun 2012 23:39:44 UTC

ender wrote:

hi, any hint will be appreciated:

obtain

from
$n^{3/2}\leq e^{k}$

but i need to express this in terms of logarithms with base 2 because is for applications into computer stuff.
i know that the answer would be

$\ln {n^{3/2}}=k$

but as i said, nedd some way to put this in terms of logarithms base 2. any idea?

thanks!

Recall that $\log_b(a)={\log a\over\log b}$ (here $\log$ is the natural log).

So if you want to write $\log x$ in terms of $\log_2$ , all you need to do is note that $\log_2 x={\log x\over\log 2}$ so $\log x=\log 2\log_2(x)$ and $\log 2$ is just some number, so this is a final answer.

S.O.S. Mathematics CyberBoard

logarithm base 2

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