You can
put this solution on YOUR website!(0.75)^n < 0.000125 where n is an integer.
I'm not supposed to use a calculator and i'm supposed to use log tables. Till now, i've taken log on both sides:
n log(0.75) < log 0.000125 . This is where i'm getting stuck. Please help.
you are perfectly correct you can continue the same way using log tables as shown below..we get n>31.24...approximately or taking integer value as asked for we get n>32.NOTE WITH CAUTION THE CHANGE OF INEQUALITY BELOW
we need n log(0.75) < log 0.000125...or n>log(0.000125) /log(0.75)..since we are deviding an inequality with log(0.75)..a negative number..so the inequality gets reversed...I trust you know how to divide the 2 numbers log(0.000125)and..log(0.75)using logs.
However, i'm not quite sure how to divide
log(0.000125)/log(0.75). Using log tables, i am getting n > 4.0969/1.8751(with a bar over 4
in the 4.0969 and a bar over 1 in 1.8751). How can one divide bar 4 and
bar 1? Thank you very much.
logs consist of 2 parts ..one characterstic which could be + or - .(-4 and -1 you mentioned)and the other one is mantissa which is always positive ,like the .0969 and .8751 you got.so if you want to devide them first transform them in to fully negative or positive numbers and then devide ..that is log0.000125=
-4+0.0969 = -3.9031 and log0.75 = -1+0.8751=-0.1249...now divide normally using logs again...
so log0.000125/log0.75=-3.9031/-0.1249=3.9031/0.1249...hope you can do it from here.
