SOLUTION: I need help solving this problem: (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 lo

Question 17622: I need help solving this problem:
(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.
Thanks a lot
Answer by venugopalramana(3286) (Show Source): 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.

RELATED QUESTIONS
I have a problem where I am supposed to write each rational expression in lowest terms... (answered by Earlsdon)

Define a relation R on the set of integers by mRn if and only if 3 divides m - n. Prove (answered by jim_thompson5910)

Dear Tutor, Could you please explain the procedure in solving this problem: Let... (answered by Fombitz)

solve m/n=p-6 for n i need help solving this problem can you help? (answered by rfer)

not sure what I need to do, i need to evaluate this problem, Evaluate: m - 6n for m = (answered by swincher4391)

can u help me on this hehe i need 3 examples of every law of exponents(FIRST TO FOURTH... (answered by josgarithmetic)

can you help me on this hehe i need 3 examples of every law of exponents(FIRST TO FOURTH... (answered by Solver92311)

can u help me on this hehe i need 3 examples of every law of exponents(FIRST TO FOURTH... (answered by Solver92311)

I really need some help on an amortization problem. I see how it is explained in the book (answered by Theo)