given that log 2=0.3010 and log 3 =0.4771. find the value of log 0.075

Question

Solving equations

Answer 1

given that log 2=0.3010 and log 3 =0.4771. find the value of log 0.075

These are all logs to the base 10.

So, log10 = 1, log 1000 = 3, etc.

 

log 0.075 = log (75/1000 ) = log 75 - log 1000 = log 75 - 3

= log 3 + log 25 - 3

= log 3 + log 5^2 - 3

= log 3 + 2.log 5 - 3

= log 3 + 2(log 10/2) - 3

= log 3 + 2(log 10 - log 2) - 3

= log 3 + 2(1 - log 2) - 3

= log 3 + 2 - 2.log 2 - 3

= log 3 - 2.log 2 - 1

= 0.4771 - 0.602 - 1

= -1.1249

Answer 2

0.075=3/40=3/(10*2^2); log0.075=log3-log10-2log2=0.4771-1-0.6020=-1.1249.