based on the estimates log(2) = .03 and log(5) = .7

Question

use properties of logarithms to find approximate values for each of the following:

log(80) 

log(0.25) 

log5(2) the 5 is a subscript

 

 

Answer 1

The values of

log (2 ) = 0.3  and log (5) = 0.7

log (80)

This can be written as

= log (16*5)

= log (16) + log 5                   [since log(ab ) = log a+ log b]

= log (2^4) + log 5  

=4 log 2 +log 5

= 4(0.3) +0.7

=1.2+0.7

=1.9.

The value of  log (80) is 1.9.

Answer 2

log (0.25)

This can be written as log (1 /4)

log (1 /4)

=  log (4^ -1)

= - log (4)

= - log (2^2)                   [log (a^m )= m log (a)]

= - 2log (2) = - 2(0.3) =  -0.6.

Hence the value of log (0.25) =  -0.6.

Answer 3

log 2 /  log 5

= 0.3 / 0.7

= 0.4286.

Hence the value of   = 0.4286.