I'm here again, now with a doubt on multiplication on logarithms, I have the expression: $(\log_5 2 + \log_5 3 \cdot\log_3 4) \cdot \log_2 5$
I've evaluated it to: $\left(\log_5 6 \cdot \dfrac{\log_5 4}{\log_5 3}\right) \cdot \dfrac{1}{\log_5 2}$
What should I do with this multiplications ?
EDIT: So, I failed miserably on algebra through, so I evaluated now to:
$= (\log_5 2 + \log5 4) * \log_2 5$
$= (\log_5 8)*\dfrac{1}{\log+5 2}$
$= \log_5(\frac{8}{2}$)
$= \log_5 4$
So, do I solved it correctly now ? Thank you. EDIT 2:
$= (\log_5 2 + \log_5 4) * \log_2 5$
$= (\log_5 8)*\dfrac{1}{\log_5 2}$
$= \dfrac{\log_5 8}{\log_5 2}$
$= \log_2 8 = 3$