Find the val of log 4 to base 5 * log 5 to base 2

In my book it is given that above is equal to log 4 to base 2. How come. I have proved log a log b = log ab
This stuff simple dives over me. I mean can u prove anythin like that?

It appears that they used the “chage of base” formula that says the

log a to the base b = (log a) / (log b)

so you can rewrite this problem as

(log 4) / (log 5) * (log 5) / (log 2)

when you multiply, the log 5 on top will cancel with the log 5 on bottom leaving (log 4) / (log 2).

if you take that answer and use the change of base formula again, you will get

log 4 with a base of 2 which is actually just 2.

I hope this helps and wasn’t too confusing,
Rousey

M/S Estonia diving – diver serch bridge for logbook

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