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:
log38⋅log39⋅1log32
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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