Based on the estimates log(2) = .03 and log(5) = .7, how do you use properties of logarithms to find approximate values for #log_5(2)#?

1 Answer
Gió
May 28, 2015

I woul change base of the logarithm using the property:
#log_bx=(log_ax)/(log_a(b))#
in your case:
#log_5(2)=(log2)/(log(5))=0.03/0.7=3/100*10/7=3/70=0.043#

Although I am not completely sure about your estimates (in particular 0.03)....the result should give you #0.43# so that #5^(0.43)=2#!

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