Suppose that u=log10(2) and v=log10(5). Find possible formulas for the following expressions in terms of u and/or v. Your answers should NOT involve any log 's.

Question

log10(2.5)=

 log10(4000)=

 log10(sqrt10)=

Answer 1

u = log2 = about .3, v =log5= about .7

10^u = 2 10^v = 5

the base is assumed to be 10 if not specified = common log

log2.5 =y, 10^y = 2.5, y= about .39794 = about .4

10^.4 = about 2.5, u = about .3 ..4 = 4u/3

10^(4u/3) = about 2.5

log4000=10log40 = about 4.6 =4.6u/3

10^(4.6u/3) = 40000

log sqr10 = about .5 = .5u/3

10^(u/6) = sqr10