1. ## logarithmic notation

Hi

Could somebody help me solve this question
(a) Express the following statements in logarithmic notation:3.375= 2.25 3/2
That's 3over2 . Thanks so much

2. ## Re: logarithmic notation

Originally Posted by cypress
Hi

Could somebody help me solve this question
(a) Express the following statements in logarithmic notation:3.375= 2.25 3/2
That's 3over2 .
$\displaystyle a = b^c$

$\displaystyle c = \log_b{a}$

3. ## Re: logarithmic notation

Thanks

But I don't understand how you got that answer...could you break it down?
I would be very greatful.Thanks

4. ## Re: logarithmic notation

Originally Posted by cypress
Thanks

But I don't understand how you got that answer...could you break it down?
I would be very greatful.Thanks
Logarithms: Introduction to "The Relationship"

5. ## Re: logarithmic notation

Originally Posted by skeeter
Thank you so much!!!

6. ## Re: logarithmic notation

cypress, what skeeter wrote was not an "answer" but the basic relationship between a logarithm and an exponential. It is impossible to give an answer to the problem you posted because you clearly did not post it correctly- there is no exponent in what you gave so it can't be converted to logarithms. Did you mean to write 3.375= 2.25^(3/2)?

7. ## Re: logarithmic notation

Originally Posted by HallsofIvy
cypress, what skeeter wrote was not an "answer" but the basic relationship between a logarithm and an exponential. It is impossible to give an answer to the problem you posted because you clearly did not post it correctly- there is no exponent in what you gave so it can't be converted to logarithms. Did you mean to write 3.375= 2.25^(3/2)?
Yes thats what i was trying to workout. Wolud you mind showing me how it's done?
Thanks

8. ## Re: logarithmic notation

Take the logarithm of both sides, therefore:
$\displaystyle \log(3,375)=\log(2,25^{\frac{3}{2}})$
Now use the following rules to continue:
$\displaystyle \log(a^b)=b\log(a)$
$\displaystyle \frac{\log(b)}{\log(a)}=\log_a(b)$

9. ## Re: logarithmic notation

Originally Posted by Siron
Take the logarithm of both sides, therefore:
$\displaystyle \log(3,375)=\log(2,25^{\frac{3}{2}})$
Now use the following rules to continue:
$\displaystyle \log(a^b)=b\log(a)$
$\displaystyle \frac{\log(b)}{\log(a)}=\log_a(b)$
Hi

I'm new to logarithms,unsure how to do the next step. Can you show me or do you know a link I could learn from?

Thanks so much

10. ## Re: logarithmic notation

If you have to solve this exercice then I thought you would know some rules about logarithms. But have you tried something with the rules I mentioned?
$\displaystyle \log(3,375)=\log(2,25^{\frac{3}{2}})$
$\displaystyle \Leftrightarrow \log(3,375)=\frac{3}{2}\log(2,25)$ (is this clear?)
$\displaystyle \Leftrightarrow \frac{\log(3,375)}{\log(2,25)}=\frac{3}{2}$

Now, apply the last rule I mentioned.

11. ## Re: logarithmic notation

Tha much is clear, can't grasp the concept of the next step :-(

12. ## Re: logarithmic notation

in your original post, you started with an exponential equation ...

$\displaystyle 3.375 = 2.25^{3/2}$

... and were asked to change it to an equation using logarithmic notation

$\displaystyle \log_{2.25}(3.375) = \frac{3}{2}$

that's all.

13. ## Re: logarithmic notation

I can understand it when I see it broken down, I find it difficult to know what rules to use.