evaluate, using logarithm table o.296× 0.0082?
I finally threw my log table book away about a year ago. I used it extensively in the late 40s until I was introduced to a slide rule that would do 5 places. Hand calculators have been a blessing. .
0.0132
0.0132
Well, if I were to evaluate that using a logarithm table, I'd probably end up getting tangled in logarithm knots and put on a logarithm show for all the logarithm clowns. But luckily, I have a better solution for you!
You can solve this using basic multiplication. Just take 0.296 and multiply it by 0.0082:
0.296 × 0.0082 = 0.0024272
So, without using a logarithm table, we've arrived at the result! Now, let's all take a moment to appreciate the logarithm clowns for their logarithmic efforts.
To evaluate the product of 0.296 and 0.0082 using a logarithm table, you can follow these steps:
1. Take the logarithm (base 10) of both numbers using the logarithm table. The logarithm of 0.296 would be determined by looking up the logarithm of 2.96 (since we moved the decimal point one place to the right) and subtracting 1. The logarithm of 0.0082 would be determined by looking up the logarithm of 82 and subtracting 4 (since we moved the decimal point four places to the left).
2. Add the logarithms together. This will give you the logarithm of the product of the two numbers.
3. Look up the antilogarithm (also known as the exponential function) of the sum you obtained in step 2 in the logarithm table. This will give you the value of the product.
For example, let's calculate it step by step:
1. Logarithm of 0.296: Find the logarithm of 2.96 in the table (let's assume it's 0.4713) and subtract 1. So, the logarithm of 0.296 is approximately -0.5287.
Logarithm of 0.0082: Find the logarithm of 82 in the table (let's assume it's 1.9138) and subtract 4. So, the logarithm of 0.0082 is approximately -2.0862.
2. Adding the logarithms: -0.5287 + (-2.0862) = -2.6149
3. Finding the antilogarithm: Look up the value corresponding to -2.6149 in the table (let's assume it's 0.003661). So, the product of 0.296 and 0.0082 is approximately 0.003661.
Please note that the values used in the example are approximations and you may need to refer to an actual logarithm table for more accurate results.
Log tables?
Scientific calculators have now existed for over 30 years.
Did a quick incomplete survey of the most common math books published in my Ontario in the last 25 years, none of them contain log tables.
The only tables still published are the "normal distribution" tables used in statistics, and some tables in actuarial math.
How old is that textbook that you are using?
Using my calculator:
let x = 0.296× 0.0082
logx = log 0.296 + log 0.0082
= -0.5287.. - 2.086186...
= -2.614894... , press 2ndF log
x = .0024272
I recall teaching this back in the 1960's using mantissas and characteristics
log 0.296 = log 2.96x 10^-1
= -1 + log 2.96 = -1 + 0.47129..
log .0082 = log 8.2 x 10^-3
= -3 + .913814
log log 0.296 + log 0.0082
= -1 + 0.47129.. + (-3 + .913814)
= -4 + 1.385104
= -3 + .385104 <--- this was always the tricky part, since we needed a positive mantissa
the anti-log of .385104 is 2.42719
and the -3 told us to move the decimal 3 places to the right, so ....
Phewww! , .... the answer is 0.0024719