Logarithms

Question

Evaluate the following. lg 1/2 + lg2/3 + lg 3/4 +...+lg 998/999 + lg 999/1000.

Answer 1

What does "lg" mean? If it means logarithm in general, what base?

 

Parviz assumed you meant "log" which is customary shorthand for "log_10", i.e., base 10 logarithms.

 

If it was a base "b", then let x = log_b(10^(-3)); then

 

b^x = 10^(-3)

 

Taking log_10 of both sides:

 

log(b^x) = log(10^(-3))

 

x log(b) = -3 log(10) = -3

 

x = -3 / log(b)

Answer 2

lg 1/2 + lg 2/3 + log 3/ 4 +               + log 999/1000

 

 

 log ( 1/2 . 2/3 . 3/4 . 4/5 ......... . 999/ 1000) = log 1/1000 = -3