Please can someone take me through it
Much appreciated
You should use the following properties of the log-function:
$\displaystyle \log(a) + \log(b) = \log(ab)$
$\displaystyle \log(a) - \log(b) = \log \left(\frac ab \right)$
$\displaystyle n \cdot \log(a) = \log(a^n)$
$\displaystyle \frac1n \cdot \log(a)=\log \left(\sqrt[n]{a} \right)$
$\displaystyle {\color{blue}\frac14 \cdot \left(\log_5(5) - \log_5(3) \right) } + \frac13 \cdot \left(\log_5(2) + \log_5(7) \right)$
$\displaystyle {\color{blue}\log_5 \left(\sqrt[4]{ \frac53 } \right) }+ \frac13 \cdot \left(\log_5(2) + \log_5(7) \right)$
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.