1. ## multiplying logs

Hi;
how do you multiply logs ie log[base2](4) * log[base2](16) I think you work out each log seperately then multiply the solution,Is this the correct process?

Here I get 8.

Also do I do the same thing with different bases?

Thanks.

2. ## Re: multiplying logs

Just use the definition like you've done.
$\displaystyle \log_a(x)=y \Leftrightarrow a^y=x$

3. ## Re: multiplying logs

Ok do I do the same thing with different bases?

4. ## Re: multiplying logs

It depends, for example if you've different bases you can use:
$\displaystyle \log_a(x)\cdot \log_x(y)=\log_a(y)$
For example:
$\displaystyle \log_2(4)\cdot \log_4(16)=\log_2(16)=4$

And offcourse you can use the definition.
$\displaystyle \log_2(4)\cdot \log_4(16)=2\cdot 2=4$

Is this clear?...

5. ## Re: multiplying logs

got to take a break from study back tommorow.

Thanks.

6. ## Re: multiplying logs

You're welcome!

7. ## Re: multiplying logs

No thats not clear.

8. ## Re: multiplying logs

What's not clear? ...

9. ## Re: multiplying logs

Until I know more will the way I did it work for the same and different bases?

10. ## Re: multiplying logs

What you did is fine, but using this log rules can be really useful sometimes. What have you learned yet about logarithms? Only the definition? ...

11. ## Re: multiplying logs

Yeah not much just doing logs now.