SOLUTION: if log0.5 = -0.3010, what is the mantissa of log0.5?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: if log0.5 = -0.3010, what is the mantissa of log0.5?      Log On


   

Question 924190: if log0.5 = -0.3010, what is the mantissa of log0.5?
Found 3 solutions by ewatrrr, MathLover1, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
log0.5 = -0.3010
log0.5 = -0.3010
1 -.301 = .699, the mantissa

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Characteristic and Mantissa:
Consider a number N+%3E+0.
Then, let the value of log+%2810%2C+N%29 consist of two parts: 0ne an integral part, the other – a proper fraction.
The integral part is called the characteristic and the fractional or the decimal part is called the mantissa.
For example, log+%2810%2C+15%29+=+1.176+=+1+%2B+0.176 => the characteristic is 1 and the mantissa is 0.176
we consider logarithms of numbers less than 1:all numbers are expressed to base 10 ; so,
log%2810%2C+0.5%29+=+-0.301+=+-1+%2B+0.699=> the characteristic is -1 and the mantissa is 0.699

Answer by Edwin McCravy(20059) About Me  (Show Source):
You can put this solution on YOUR website!
if log0.5 = -0.3010, what is the mantissa of log0.5?

Wow!  Who is still doing work with logarithm tables?

Here is how it was done in the old days:

We added the equation to the equation 0 = 10.0000 - 10 which 
amounted to adding to zero: 

        0 = 10.0000 - 10
   log0.5 = -0.3010 
   ---------------------
   log0.5 =  9.6990 - 10

So the mantissa is the decimal digits .6990.
The characteristic is -1, since 0.5 = 5×10-1 the
power of 10 in the scientific notation for the number.

--------------------------------------------------------- 

We did this sort of thing 50+ years ago before electronic calculators
were invented, back when there were no cell phones and the only
computers were huge and had no video screens.  We used logarithm tables
to multiply and divide in complicated calculations. I am shocked to 
see somebody still doing this today.  With modern calculators there 
is no need for this very ancient type of calculation. I would be 
interested to know who is still teaching this.  Is it a part of 
a mathematical history course?

Edwin