How To Find Value Of Log 2 From Log Table

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Before computers and calculators, logarithms were quickly calculated using logarithmic tables.^[ane] These tables tin nonetheless be useful for quickly calculating logarithms or multiplying large numbers, once you figure out how to employ them.

1
Cull the correct table. To find log_a(north), yous'll need a log_a table. Most log tables are for base of operations-ten logarithms, called "common logs."^[2]
- Example: log_x(31.62) requires a base-x table.
2
Find the right prison cell. Look for the jail cell value at the post-obit intersections, ignoring all decimal places:^[iii]
- Row labeled with first 2 digits of n
- Cavalcade header with third digit of northward
- Example: log₁₀(31.62) → row 31, column 6 → jail cell value 0.4997.
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3
Use smaller nautical chart for precise numbers. Some tables take a smaller set of columns on the right side of the nautical chart. Use these to adjust answer if n has iv or more pregnant digits:
- Stay in same row
- Find small column header with fourth digit of north
- Add this to previous value
- Instance: log_ten(31.62) → row 31, small column 2 → cell value 2 → 4997 + 2 = 4999.
4
Prefix a decimal point. The log tabular array only tells yous the portion of your answer after the decimal bespeak. This is called the "mantissa."^[four]
- Example: Solution so far is ?.4999
5

Notice the integer portion. Also called the "characteristic". By trial and error, notice integer value of p such that $a^{p}<n$ and $a^{p+one}>n$ .

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i
Sympathise what a logarithm is. x² is 100. x^three is 1000. The powers 2 and 3 are the base-10 logarithms of 100 and 1000.^[v] In general, a^b = c tin exist rewritten equally log_ac = b. And then, proverb "x to the power of 2 is 100" is equivalent to saying "the base-ten log of 100 is ii." Each logarithmic table is only usable with a sure base (a in the equation above). By far the most mutual type of log table uses base-x logs, also called the common logarithm.
- Multiply two numbers past adding their powers. For example: ten² * ten³ = ten⁵, or 100 * 1000 = 100,000.
- The natural log, represented by "ln", is the base of operations-e log, where east is the constant 2.718. This is a useful number in many areas of math and physics. You can utilise natural log tables in the aforementioned way that you utilise common, or base-10, log tables.
2

Identify the characteristic of the number whose log you want to find. Let'south say you want to notice the base-10 log of 15 on a common log tabular array. fifteen lies betwixt 10 (10ⁱ) and 100 (10²), and then its logarithm will lie between one and 2, or be 1.something. 150 lies between 100 (ten²) and 1000 (10³), so its logarithm will lie betwixt 2 and 3, or exist 2.something. The .something is called the mantissa; this is what you volition discover in the log tabular array. What comes before the decimal signal (1 in the start example, 2 in the second) is the characteristic.
3
Slide your finger down to the appropriate row on the table using the leftmost column. This column will show the get-go two or, for some big log tables, iii digits of the number whose logarithm you're looking up. If y'all're looking upwardly the log of 15.27 in a normal log tabular array, get to the row marked fifteen. If you're looking upwardly the log of 2.57, become to the row marked 25.
- Sometimes the numbers in this row will have a decimal point, so you'll await up ii.5 rather than 25. You lot can ignore this decimal indicate, every bit it won't bear on your reply.
- Too ignore whatever decimal points in the number whose logarithm you lot're looking up, as the mantissa for the log of one.527 is no different from that of the log of 152.7.
four

On the advisable row, slide your finger over to the appropriate column. This column will exist the one marked with the side by side digit of the number whose logarithm yous're looking up. For case, if you want to discover the log of 15.27, your finger will be on the row marked 15. Slide your finger along that row to the right to discover column 2. You volition be pointing at the number 1818. Write this downward.
5

If your log table has a mean difference table, slide your finger over to the cavalcade in that table marked with the next digit of the number you're looking up. For 15.27, this number is 7. Your finger is currently on row 15 and column two. Slide information technology over to row 15 and mean differences column 7. You will be pointing at the number 20. Write this down.
6

Add the numbers found in the two preceding steps together. For fifteen.27, yous will get 1838. This is the mantissa of the logarithm of 15.27.
vii

Add the characteristic. Since fifteen is between 10 and 100 (10ⁱ and 10^two), the log of fifteen must exist between 1 and two, so 1.something, so the characteristic is ane. Combine the characteristic with the mantissa to become your final answer. Find that the log of fifteen.27 is 1.1838.

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1
Sympathise the anti-log table. Use this when you have the log of a number only not the number itself. In the formula 10^north = x, northward is the common log, or base-x log, of 10. If you have x, find n using the log table. If yous have north, find x using the anti-log table.
- The anti-log is likewise ordinarily known as the changed log.
ii

Write down the characteristic. This is the number earlier the decimal point. If you lot're looking up the anti-log of two.8699, the feature is ii. Mentally remove information technology from the number you're looking up, but make sure to write it down so yous don't forget it - it volition be important later.
iii

Find the row that matches the first part of the mantissa. In 2.8699, the mantissa is .8699. Most anti-log tables, like most log tables, have two digits in the leftmost column, so run your finger down that column until you discover .86.
four

Slide your finger over to the column marked with the next digit of the mantissa. For 2.8699, slide your finger along the row marked .86 to notice the intersection with cavalcade 9. This should read 7396. Write this downwards.
5

If your anti-log table has a tabular array of hateful differences, slide your finger over to the column in that table marked with the adjacent digit of the mantissa. Make sure to keep your finger in the same row. In this example, yous will slide your finger over to the terminal column in the table, column 9. The intersection of row .86 and mean differences column 9 is xv. Write that downward.
half-dozen

Add together the ii numbers from the two previous steps. In our case, these are 7396 and 15. Add them together to go 7411.
7

Use the characteristic to place the decimal point. Our characteristic was 2. This means that the reply is between ten² and x³, or betwixt 100 and 1000. In gild for the number 7411 to fall between 100 and 1000, the decimal bespeak must go afterwards 3 digits, so that the number is almost 700 rather than 70, which is too pocket-size, or 7000, which is besides big. So the terminal answer is 741.1.

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one

Sympathize how to multiply numbers using their logarithms. We know that x * 100 = 1000. Written in terms of powers (or logarithms), 10¹ * 10² = 10³. We also know that ane + ii = 3. In general, 10^ten * ten^y = ten^{ten + y}. So, the sum of the logarithms of two dissimilar numbers is the logarithm of the production of those numbers. We tin multiply two numbers of the same base by adding their powers.^[vi]
2

Expect upwardly the logarithms of the two numbers you desire to multiply. Use the method above to observe the logarithms. For example, if you want to multiply 15.27 and 48.54, you would detect the log of 15.27 to be ane.1838 and the log of 48.54 to be 1.6861.
3

Add together the two logarithms to find the logarithm of the solution. In this case, add 1.1838 and ane.6861 to become 2.8699. This number is the logarithm of your answer.
4

Await up the anti-logarithm of the result from the in a higher place step to notice the solution. You tin can do this by finding the number in the body of the table closest to the mantissa of this number (8699). The more than efficient and reliable method, however, is to find the answer in the tabular array of anti-logarithms, every bit described in the method above. For this instance, you lot volition get 741.ane.

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Add New Question

Question

How do I observe the log of a cube?

Triple the log of the number that has been cubed.
Question

How practise I find logs for three.xiv?

Multiply 3.14 with 10 to get 31.4, and then find log (31.4), which is roughly 1.4969. Now, divide this past x to get your log with base of operations x.
Question

How do I notice the log of a single digit?

Say you want to notice the log of nine. You know that 9 = 9.0 = 9.00 and so on. At present that you lot have the right number of significant digits, you can use a log table equally long as y'all bargain with decimal points correctly.
Question

How tin can one find the log of 3.5?

3.5 = three.50 (with as many 0's every bit y'all want.) You now have enough significant digits to follow method 2 in the commodity.
Question

If I have divided numbers using log, then how exercise I use an antilog?

As long as the quotient is an exponent, you lot can use the normal method to find the antilog.
Question

How exercise we notice the logarithm of 2000?

Find the log 2000=.1585. Then add together 3 every bit 2000 is betwixt chiliad and 10000. Answer is 3.1585.
Question

How can I make my ain log table when I don't accept a log book?

Choose the base you want to use. Write the numbers ten-99 down the left side and the numbers 0-nine across the summit. Employ a calculator or spreadsheet to summate the log for each space in the table.
Question

How do I discover log(0.0046)?

You can express this as 46 10 10 to the power -iii. The next step is to find log(46), then multiply it with 10 to the power -3.
Question

How exercise I notice the cube of 288 using the logarithmic tables?

Balaaji Selvanathan

Community Reply

288^1/3 = 10 1/3 log(288)=log x one/iii(two.459)=log 10 0.819=log ten x=Al(0.819)=6.603(approx)
Question

How practice I find anti-log -3.746?

Joab Kalyegira

Community Answer

Express the log as negative characteristic minus the mantissa -three-0.746. Decrease i from characteristic and add 1 to the mantissa in order to make it positive; if yous're using a log table, -3 - ane - 0.746 + 1. Write the result equally a log having a negative characteristic and a positive mantissa -4 + 0.254. So use the log table to find the anti-log. Anti-log of -iii.746 is 1.795x10^-four = 0.0001795.

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Always do the calculations on a canvass of paper and not mentally, as these are large and complicated numbers and they tin become tricky.
Read the page heading carefully. A log book has about 30 pages and using the wrong page will give the wrong answer.

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Utilize the methods described in this article for common log, or base of operations-10 log, tables, and make certain the numbers yous're looking upwards are in base-ten format, or scientific notation.
Almost tables are but authentic to three or four digits. If you find the anti-log of 2.8699 using a computer, the answer will round to 741.2, but the answer you become using log tables is 741.1. This is due to rounding in the tables. If you need a more precise reply, utilise a figurer or another method rather than log tables.
Make sure that the readings are from the aforementioned row. Sometimes, nosotros may mix up rows and columns because of the modest size and shut spacing.

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logarithmic table or log book
spare sheet of paper.

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Article Summary X

To use logarithmic tables for a base-10 logarithm, start past making sure yous have the correct log table, called a "common log." So, scan the "n" column on the far left for the commencement two digits of the number. From in that location, move to the right to find the column labeled with the tertiary digit of the number, and find the cell where the row and cavalcade intersect. The prison cell contains the digits of the number that are after the decimal point, or the "mantissa." In one case yous have the mantissa, count the number of places subsequently the decimal betoken and subtract 1 to find the integer. If you need to acquire more, such as how to discover the anti-log of your logarithm, keep reading the article!

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