Question

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)`?

Answer 1

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`!