# Thread: how to get from ln(4)/2 to ln2 ?

1. ## how to get from ln(4)/2 to ln2 ?

Hi

I have an equation $\displaystyle e^{2t} = 4$

So to solve I do this:

$\displaystyle 2t = ln4$

$\displaystyle t = ln4/2$

That's fine, but answer is t = ln2. How do you get from ln2?

I can see that ln(4)/2 is equivalent to ln2 - but what is algebra to get to ln2?

Angus

2. ## Re: how to get from ln(4)/2 to ln2 ?

Originally Posted by angypangy
Hi

I have an equation $\displaystyle e^{2t} = 4$

So to solve I do this:

$\displaystyle 2t = ln4$

$\displaystyle t = ln4/2$

That's fine, but answer is t = ln2. How do you get from ln2?

I can see that ln(4)/2 is equivalent to ln2 - but what is algebra to get to ln2?

Angus
Apply the identity $\displaystyle \ln \sqrt{a}= \frac{\ln a}{2}$...

Marry Christmas from Serbia

$\displaystyle \chi$ $\displaystyle \sigma$

3. ## Re: how to get from ln(4)/2 to ln2 ?

Originally Posted by chisigma
Apply the identity $\displaystyle \ln \sqrt{a}= \frac{\ln a}{2}$...

Marry Christmas from Serbia

$\displaystyle \chi$ $\displaystyle \sigma$

4. ## Re: how to get from ln(4)/2 to ln2 ?

$\displaystyle a \log(b)= \log(b^a)$

5. ## Re: how to get from ln(4)/2 to ln2 ?

Originally Posted by angypangy
$\displaystyle \frac{\ln 4}{2}= \ln \sqrt{4}= \ln 2$

Marry Christmas from Serbia

$\displaystyle \chi$ $\displaystyle \sigma$

6. ## Re: how to get from ln(4)/2 to ln2 ?

Originally Posted by chisigma
$\displaystyle \frac{\ln 4}{2}= \ln \sqrt{4}= \ln 2$

Marry Christmas from Serbia

$\displaystyle \chi$ $\displaystyle \sigma$
So it is like this?

$\displaystyle \frac{\ln 4}{2}= \frac{1}{2} * ln4 = ln4^\frac{1}{2} = ln2$

7. ## Re: how to get from ln(4)/2 to ln2 ?

or ...

$\displaystyle \frac{\ln{4}}{2} = \frac{\ln{2^2}}{2} = \frac{2\ln{2}}{2} = \ln{2}$

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# ln4/2 ln 2

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