# Math Help - solving this log

1. ## solving this log

Please can someone take me through it
Much appreciated

2. Originally Posted by 200001

Please can someone take me through it
Much appreciated
You should use the following properties of the log-function:

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

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

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

$\frac1n \cdot \log(a)=\log \left(\sqrt[n]{a} \right)$

3. Hi
thanks
Im ok with the laws of logs but cant seem to get this one going for some reason

4. Originally Posted by 200001

Please can someone take me through it
Much appreciated
$\frac{1}{4}\,log_5 \left(\frac{5}{3}\right) + \frac{1}{3}log_5 \left(2 \cdot 7\right)$

5. Originally Posted by 200001
Hi
thanks
Im ok with the laws of logs but cant seem to get this one going for some reason
${\color{blue}\frac14 \cdot \left(\log_5(5) - \log_5(3) \right) } + \frac13 \cdot \left(\log_5(2) + \log_5(7) \right)$

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

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.