# multiplying logs

• August 28th 2011, 10:33 AM
anthonye
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.
• August 28th 2011, 10:47 AM
Siron
Re: multiplying logs

Just use the definition like you've done.
$\log_a(x)=y \Leftrightarrow a^y=x$
• August 28th 2011, 10:50 AM
anthonye
Re: multiplying logs
Ok do I do the same thing with different bases?
• August 28th 2011, 10:54 AM
Siron
Re: multiplying logs
It depends, for example if you've different bases you can use:
$\log_a(x)\cdot \log_x(y)=\log_a(y)$
For example:
$\log_2(4)\cdot \log_4(16)=\log_2(16)=4$

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

Is this clear?...
• August 28th 2011, 11:15 AM
anthonye
Re: multiplying logs
got to take a break from study back tommorow.

Thanks.
• August 28th 2011, 11:31 AM
Siron
Re: multiplying logs
You're welcome! :)
• August 28th 2011, 01:19 PM
anthonye
Re: multiplying logs
No thats not clear.
• August 28th 2011, 01:47 PM
Siron
Re: multiplying logs
What's not clear? ...
• August 28th 2011, 01:52 PM
anthonye
Re: multiplying logs
Until I know more will the way I did it work for the same and different bases?
• August 28th 2011, 01:56 PM
Siron
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? ...
• August 28th 2011, 01:59 PM
anthonye
Re: multiplying logs
Yeah not much just doing logs now.