MHB How can I simplify this logarithm?

Elena1
Messages
24
Reaction score
0
$$\log_{2}\left({24}\right) / \log_{96}\left({2}\right) - \log_{2}\left({192}\right) /\log_{12}\left({2}\right)$$
 
Last edited by a moderator:
Mathematics news on Phys.org
Elena said:
$$\log_{2}\left({24}\right) / \log_{96}\left({2}\right) - \log_{2}\left({192}\right) /\log_{12}\left({2}\right)$$

Hi Elena! :)

How far can you get?

Perhaps you can substitute the following? (Wondering)
$$\log_b y = \frac{\log_2 y}{\log_2 b}$$
That should make the expression simpler...

So for instance:
$$\log_{96} 2 = \frac{\log_2 2}{\log_2 96} = \frac{1}{\log_2 96}$$
 
Last edited:
actually i can` t understand this subject can you explain more?please
 
I think what I like Serena meant is:

$$\log_{96}(2)=\frac{\log_2(2)}{\log_2(96)}=\frac{1}{\log_2(96)}$$

This is an application of the change of base formula.
 
i know this...in the end of book i have the solution 3 but i obtained 0 the result
 
Elena said:
i know this...in the end of book i have the solution 3 but i obtained 0 the result

Good!
Can you show the first intermediate step? (Wondering)
 
$$\log_{2}\left({6*{2}^{2}}\right) /\log_{6*{2}^{4}}\left({2}\right) -\log_{2}\left({3*{2}^{6}}\right)/ \log_{3*{2}^{2}}\left({2}\right)$$

- - - Updated - - -

finally i obtained $$4 \log_{2}\left({6}\right) / \frac{1}{8}\log_{6}\left({2}\right) -6\log_{2}\left({6}\right) /
\frac{1}{2}\log_{6}\left({2}\right)$$
 
Last edited by a moderator:
Elena said:
$$\log_{2}\left({6*{2}^{2}}\right) /\log_{6*{2}^{4}}\left({2}\right) -\log_{2}\left({3*{2}^{6}}\right)/ \log_{3*{2}^{2}}\left({2}\right)$$

Good!

Can you change the base of each logarithm to $2$?

Btw, I have added $$$$ tags around your formula to properly render it.

Elena said:
finally i obtained $$4 \log_{2}\left({6}\right) / \frac{1}{8}\log_{6}\left({2}\right) -6\log_{2}\left({6}\right) /
\frac{1}{2}\log_{6}\left({2}\right)$$

That doesn't look quite right.
Let's zoom in on $\log_{6*{2}^{4}}\left({2}\right)$
It appears you deduced that it is equal to $\frac{1}{8}\log_{6}\left({2}\right)$

How did you get that? (Wondering)
 
$$\log_{6*{2}^{4}}\left({2}\right)=\frac{1}{4}\log_{3*{2}^{2}}\left({2}\right)=\frac{1}{8}\log_{6}\left({2}\right)$$
how can i write to be clear?
 
Last edited:
  • #10
Elena said:
$$$$ \log_{6{2}^{4}}\left({2}\right)=\frac{1}{4}\log_{3*{2}^{2}}\left({2}\right)=\frac{1}{8}\log_{6}\left({2}\right)$$$$

You need to include $\LaTeX$ code within tags. On our toolbar you will see a button labeled with the $\Sigma$ character. Click this button and the MATH tags will be inserted at your current cursor location within the post message. Then, in between these tags (the cursor is already conveniently placed there) type your code. This will cause the code to be parsed correctly. :D
 
  • #11
Elena said:
$$$$\log_{6{2}^{4}}\left({2}\right)=\frac{1}{4}\log_{3*{2}^{2}}\left({2}\right)=\frac{1}{8}\log_{6}\left({2}\right)
Code:
how can i write to be clear?

I see you have included $$$$ tags now.
However the $$ tag must go at the beginning, and the $$ must go at the end.
 
  • #12
Elena said:
$$\log_{6*{2}^{4}}\left({2}\right)=\frac{1}{4}\log_{3*{2}^{2}}\left({2}\right)=\frac{1}{8}\log_{6}\left({2}\right)$$
how can i write to be clear?

It should be:
$$\log_{6\cdot{2}^{4}}\left({2}\right)
=\frac{\log_6(2)}{\log_6(6\cdot {2}^{4})}
=\frac{\log_6(2)}{\log_6(6) + \log_6({2}^{4})}
=\frac{\log_6(2)}{1 + 4\log_6(2)}$$

Or better:
$$\log_{6\cdot{2}^{4}}\left({2}\right)
=\log_{3\cdot{2}^{5}}\left({2}\right)
=\frac{\log_2(2)}{\log_2(3\cdot {2}^{5})}
=\frac{1}{\log_2(3) + \log_2({2}^{5})}
=\frac{1}{\log_2(3) + 5}
$$
 

Similar threads

Back
Top