SOLUTION: I am not remembering how to solve this type of problem : Log 2 is similar to 0.301 and log 5 is similar to 0.699. What is the approximate value of the expression log 8/125?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I am not remembering how to solve this type of problem : Log 2 is similar to 0.301 and log 5 is similar to 0.699. What is the approximate value of the expression log 8/125?      Log On


   



Question 310861: I am not remembering how to solve this type of problem :
Log 2 is similar to 0.301
and log 5 is similar to 0.699.
What is the approximate value of the expression log 8/125?

Found 2 solutions by Earlsdon, scutechandni10:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
If Log%282%29+=+0.301%29 Approx. and...
If Log%285%29+=+0.699 Approx. Find...
Log%288%2F125%29+=+Log%288%29-Log%28125%29 Substitute 8+=+2%5E3 and 125+=+5%5E3 so...
Log%282%5E3%29-Log%285%5E3%29+=+3Log%282%29-3Log%285%29 and...
3Log%282%29-3Log%285%29+=+3%280.301%29-3%280.699%29=0.903-2.097+=+-1.194

Answer by scutechandni10(7) About Me  (Show Source):
You can put this solution on YOUR website!
Given that log2=0.0301 and log5=0.699
then;
log 8/125= log2^3/log5^3
= 3log2/3log5
= (3log2)-(3log5)
=3(0.0301)-3(0.699)
=0.903-2.097
log8/125=-1.194