if u=log(2), and v=log(5) --find possible formulas for the following expressions in terms of v and u. No logs in your answers. 1. log(.025)= 2.log(80)=

Answer 1

A key ability to have when you are working with logarithms comes from the understanding of the basic rules:

1) log(m*n) = log(m) + log(n)

2) log(m/n) = log(m) - log(n)

3) log(m^n) = nlog(m)

4) log(1) = 0

So also, recognize that log(0.025) is log(1/40)

Applying the rules, log(1/40) = log(1) - log(40) = 0 - log(8*5) = 0 - log(2³*5) = 0 - (log(2³) + log(5)) = 0 - (3log(2) + log(5)) = 0 - (3u + v) = -3u - v

For 2) recognize that log(80) = log(16*5) = log(2⁴*5) = log(2⁴) + log(5) = 4log(2) + log(5) = 4u + v