Wednesday, 22 October 2014

logarithms - Logs - changing the base to evaluate



Just a bit confused about how to evaluate the following





log38×log59×log25




What I have done so far:



I have used the change of base rule to change each log to base 3, so I ended up with this after cancelling:
log38log391log32



First of all, I'm not even sure that I have made the right decision in changing to base 3, does it matter what you change to? Second of all, I'm just unsure where to go from here.


Answer




To systematically attack such questions, use logxy=logylogx i.e.
log38=ln8ln3,log59=ln9ln5,log25=ln5ln2
multiply and simplify
log38×log59×log25=ln8ln3×ln9ln5×ln5ln2=ln8×ln9ln3×ln2=ln8ln2×ln9ln3=3×2=6


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