Log and Antilog are widely used in mathematics. A log is the shortened form of logarithm and an Antilog is the shortened form of antilogarithm. A log is the inverse process of exponent while antilog is the inverse process of a log.
Log and Antilog are widely used in mathematics, chemistry, physics, and even in excel and python. Log and Antilog are very essential for the solution of various complicated problems.
What is the purpose of Log?
The other way to express exponent is known as a logarithm. In simple words, we can say that the inverse process of exponents is said to be the logarithm. Log expression is used to answer the question of mathematical expressions that how many times a number is multiplied to itself to get the required number?
For example, how many times 3 is multiplied to itself to get 81?
To make lengthy, complicated, and complex calculations easy and simple, we convert the form of number by using log.
The expression of logarithm is,
Logb a = x
Which is derived from bx = a.
Rules of Logarithm
| Names of rules | Results |
| Product Rule | ln(ab) = ln(a) + ln(b) |
| Quotient Rule | ln(a/b) = ln(a) – ln(b) |
| Power Rule | ln(a2) = 2ln(a) |
| Identity Rule | Logb b = b |
| Log of e | ln(e) = 1 |
| Log of one | ln (1) = 0 |
| Log of reciprocal | ln(1/x) = – ln(x) |
| Log of zero | ln (0) = undefined |
How to calculate the logarithm?
A logarithm is the reverse of the exponents. A logarithm is used to reduce the difficulty of writing confusing numbers simply.
Example 1
Find the logarithm of 36 has base 2?
Solution
Step 1: Write the given numbers in the form of a logarithm expression.
Log2 36
Step 2: To calculate convert the number in product form.
Log2 36 = Log2 (9 x 4)
Step 3: Apply the product rule of the logarithm.
Log2 36 = Log2 (9) + Log2 (4)
Step 4: Now make the numbers in exponent form.
Log2 36 = Log2 (32) + Log2 (22)
Step 5: apply power rule.
Log2 36 = 2Log2 (3) + 2Log2 (2)
Step 6: Apply identity rule.
Log2 36 = 2Log2 (3) + 2(2)
Log2 36 = 2(1.585) + 2(2)
Log2 36 = 7.17
Example 2
Find the logarithm of 128 have base 2?
Solution
Step 1: Write the given numbers in the form of a logarithm expression.
Log2 128
Step 2: To calculate convert the number in product form.
Log2 128 = Log2 (16 x 8)
Step 3: Apply the product rule of the logarithm.
Log2 128 = Log2 (16) + Log2 (8)
Step 4: Now make the numbers in exponent form.
Log2 128 = Log2 (24) + Log2 (23)
Step 5: apply power rule.
Log2 128 = 4Log2 (2) + 3Log2 (2)
Step 6: Apply identity rule.
Log2 128 = 4(2) + 3(2)
Log2 128 = 8 + 6
Log2 128 = 14
What is Antilog?
Antilog is the reverse process of the log. In simple words, lengthy, complicated, and complex calculations are converted in logarithm to make them simple, to get back to the original form use antilog.
When the numbers are to be handled easily even larger numbers or smaller numbers, use antilog. The compressed number of the logarithm is converted back to its original form by using an antilog operator.
The expression for antilog is simple as to raise the logarithm to its base. For example, antilog of y = log10 5 = 105.
How to calculate Antilog?
Antilogarithm is the reverse of the logarithm. Antilog can be calculated by using the antilog table. You can also use the antilog calculator for the calculations for the antilog problem accurately.
Example 1
Find the antilog for base 2 and the log value 6.
Solution
Step 1: Identify the values from the given problem.
Base (b) = 2
Log value = 6
Step 2: Use in antilog expression.
Antilog2 6 = by
Antilog2 6 = 26
Antilog2 6 = 2 x 2 x 2 x 2 x 2 x 2
Antilog2 6 = 64
Example 2
Find the antilog for the base 10 and the log value 8.
Solution
Step 1: Identify the values from the given problem.
Base (b) = 10
Log value = 8
Step 2: Use in antilog expression.
Antilog10 8 = by
Antilog10 8 = 108
Antilog10 8 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
Antilog10 8 = 100000000
Example 3
Find the antilog for the base 5 and the log value 8.
Solution
Step 1: Identify the values from the given problem.
Base (b) = 5
Log value = 8
Step 2: Use in antilog expression.
Antilog5 8 = by
Antilog5 8 = 58
Antilog5 8 = 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5
Antilog5 8 = 390625
Difference between Log and Antilog
A log is the reverse process of the exponent, while an antilog is the reverse process of the logarithm. A log is used to convert the confusing number easily, whole antilog is used to get back the original number of the log by converting it again in the confusing number.
The logarithm has a general formula and some basic rules to convert the numbers easily. on the other hand, antilog used a table and convert them in the best form. antilog also used the process to calculate just take log number and put it in the power of the base.
Summary
Log and antilog stand for logarithm and antilogarithm respectfully. Both the terms are widely used in many branches of science such as mathematics, physics, chemistry, and many other branches of science.
The process of finding these terms is simple. Both the terms are used for making the problem simpler. Log and antilog are the reverse processes of the exponent and the logarithm respectfully. To take command in both terms make sure to practice it by hand.
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