# solving this log

• Feb 10th 2010, 10:11 AM
200001
solving this log
http://img692.imageshack.us/img692/9857/logd.jpg

Please can someone take me through it
Much appreciated (Happy)
• Feb 10th 2010, 10:21 AM
earboth
Quote:

Originally Posted by 200001
http://img692.imageshack.us/img692/9857/logd.jpg

Please can someone take me through it
Much appreciated (Happy)

You should use the following properties of the log-function:

$\displaystyle \log(a) + \log(b) = \log(ab)$

$\displaystyle \log(a) - \log(b) = \log \left(\frac ab \right)$

$\displaystyle n \cdot \log(a) = \log(a^n)$

$\displaystyle \frac1n \cdot \log(a)=\log \left(\sqrt[n]{a} \right)$
• Feb 10th 2010, 10:26 AM
200001
Hi
thanks
Im ok with the laws of logs but cant seem to get this one going for some reason
• Feb 10th 2010, 10:35 AM
e^(i*pi)
Quote:

Originally Posted by 200001
http://img692.imageshack.us/img692/9857/logd.jpg

Please can someone take me through it
Much appreciated (Happy)

$\displaystyle \frac{1}{4}\,log_5 \left(\frac{5}{3}\right) + \frac{1}{3}log_5 \left(2 \cdot 7\right)$
• Feb 10th 2010, 10:35 AM
earboth
Quote:

Originally Posted by 200001
Hi
thanks
Im ok with the laws of logs but cant seem to get this one going for some reason

$\displaystyle {\color{blue}\frac14 \cdot \left(\log_5(5) - \log_5(3) \right) } + \frac13 \cdot \left(\log_5(2) + \log_5(7) \right)$

$\displaystyle {\color{blue}\log_5 \left(\sqrt[4]{ \frac53 } \right) }+ \frac13 \cdot \left(\log_5(2) + \log_5(7) \right)$

I've transformed the first summand according the laws of logarithms. I'll leave the second summand for you. Afterwards combine both summands to get one term.