# 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)?

Based on the estimates $\mathrm{log}\left(2\right)=.03$ and $\mathrm{log}\left(5\right)=.7$, how do you use properties of logarithms to find approximate values for ${\mathrm{log}}_{5}\left(2\right)$?
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Caiden Brewer
I woul change base of the logarithm using the property:
${\mathrm{log}}_{b}x=\frac{{\mathrm{log}}_{a}x}{{\mathrm{log}}_{a}\left(b\right)}$
${\mathrm{log}}_{5}\left(2\right)=\frac{\mathrm{log}2}{\mathrm{log}\left(5\right)}=\frac{0.03}{0.7}=\frac{3}{100}\ast \frac{10}{7}=\frac{3}{70}=0.043$
Although I am not completely sure about your estimates (in particular 0.03)....the result should give you 0.43 so that ${5}^{0.43}=2!$