resolving logarithm without calculator?

Question

i want to know is there any way to resolve logarithm without calculator , because we shouldnt use calculator in our exams, and sometimes there are some kind of troubles:

(log 3.17 ) how can i resolve it without calculator??????!!!!

I dont want to use calculator
i know the result

Answer 1

The simple fact of the matter is that you can't.

log(3.17) is equivalent to finding the value of x for

10^x = 3.17

It just can't be done, and if you're asked to solve this on a test without a calculator then this is entirely unreasonable.

There ARE logarithms that you resolve without a calculator; take this one, for instance.

log[base 2] (1/128)

Let x = log[base 2](1/128). Then
2^x = 1/128
2^x = 1/2^7
2^x = 2^(-7)
Therefore, x = -7 (we equate the powers).

Here's another example where you don't use a calculator:

3^x = 27^(2x + 1)
3^x = (3^3)^(2x + 1)
3^x = 3^(6x + 3)

Therefore,

x = 6x + 3
-3 = 5x
x = -3/5

The key thing to know here is that we had numbers which worked out perfectly, in that both sides of the equation were the same powers. log(3.17) does NOT have this property, and you HAVE to use a calculator.

Answer 2

Well, often in examinations you will be given logarithmic tables and sometimes even some formulae in a booklet. I suggest you learn to read logarithmic tables.
If not and you want logarithms with calculation alone, you may try the Taylor expansion for log (1+z) and make suitable substitutions to obtain a series for any logarithm. Of course you will have to add many terms for many required degrees of accuracy, making the table alternative much more lucrative and indeed viable.

Answer 3

generally you cant.

for some values of the arg of the log it is possib;e todo without calculator.

for instance for 100, because 10^2 = 100 so log (100 ) = 2

if the base of your log is 2 you can do log1/64 = -6, since 1/64 = 2^(-6)

Answer 4

I think there are some logarithm tables and there are also some kind of rulers that have a sliding part over the number and its logarithm. You should ask about possiblility of taking them into your exam.

Answer 5

what you can do is approximate :) basically from the definition of logarithm in your case we get that
10^x=3.17 (ten to the power of x is 3.17)
x belongs to [0,1].
Let's try with 0.5. We obtain 10^(0.5) which is sqrt(10) which seems to be close to 3.17. So we can check it.
3.17*3.17=10.0489 which is a fair approx.

One good hint: learn by heart only roots of 2,3,5,7 :) and with them you can count roots of bigger numbers like of 10 because sqrt(10)=sqrt(2)*sqrt(5). Good luck with exams!

Answer 6

is this log with base 10? if yes this a little over 1/2.

Answer 7

there are some qns tt u don't need the calculator, such as when the log cancel out on each side when they have the same base..

Answer 8

use log tables instead.