Solutions

Problem Set #6:

In what follows, suppose that it is given that the following are true

log(2) = .3 log(3) = .48 log(5) = .7 log(7) = .85

Use these facts, if applicable, and properties of logs and algebra to provide values for: (no calculators!)

a) log(1000) = log10³ = 3 log10 = 3(1) = 3

b) log(6) = log(2*3) = log2 + log3 = .3 + .48 = .78

c) log(9) = log3² = 2log3 = 2(.48) = .96

d) log(1/2) = -log(2) = -.3

e) log(7/5) = log7 - log5 = .85 - .7 = .15

f) log(30) = log(3*10) = log3 + log10 = .48 + 1 = 1.48

g) log(81) =log9² = 2log9 = 2(.96) (see part c)

Next, use algebra and log properties to simplify each expression:

h) 10^log(2) = 2

i) 10^-log(5) = 1/5

j) 100^log(3) = 9

k) 1000^log(2) = 8

If the Richter scale is a logarithm of the energy associated with an earthquake, can you explain why a change of 1 in its value for one earthquake vs another is so significant? This means the energy changes by a factor of 10