LCM Calculator
Our Antilog calculator finds the antilog value for any base and exponent in a matter of seconds by using the Antilogarithm function. Antilogarithm is the inverse of the logarithm function.
This antilogarithm calculator gives the inverse log values for different bases like the “10 or e” in a single click and makes the antilog calculation easy.
What is Antilog?
Antilog is the abbreviation of the “Antilogarithm”. It is the inverse process of the logarithm that is used to find the original value whose logarithm is already determined.
To find the original number using the inverse logarithm function. The inverse logarithm function is represented as “Log-1” or the “Antilogba”.
Mathematically defined as,
“If “logb(x) = y”, where “y” is the log (logarithm) of “x” with the base “b” then antilog (antilogarithm) of “y” with the base “b” is equal to “x” represented as “Antilogb(y) = x”.”
For example: The antilog of “2” with base “10” is antilog10 (2) =100 while the log of 100 with base “10” is “2” written as (log10(100) = 2).
Antilog Formula
As discussed above, Antilog is the inverse of a log while the log is an inverse process of exponents, thus overall antilog is equal to the exponent. Thus the antilog formula in the exponent form can be stated as:
If: logbx = y; then ⟹ Antilog by = by
How to find Antilog?
To find the antilog of any numbers with any base use the antilog equation and simply use the antilog formula in the exponent form. Alternatively, use our inverse log calculator to evaluate its value.
The equation that used to find antilog is given below:
X = Antilogb (logbx)
X = Antilogb(y)
Simply, take the logarithm value as an exponent of the base.
X = by
Where:
- X= Shows the Antilog value
- b = represent base of antilog
- Y = represents log value
Steps to Calculate the Antilog
To find the antilog value manually with the help of the above antilog formula follow the below steps.
- First note the base and exponent to calculate the antilog of any number “X”.
- Put the exponent (y) and base (b) values in the antilog formula i.e. X = by.
- Get the final antilog value simplified the “by” using algebraic techniques.
Here, solve the manual example with detailed steps that help to understand the use of the antilog formula and its calculation.
Example 1
Calculate the antilog for the log/exponent value 4 with the base 10.
Solution
Step 1: Note the value of the base and exponent from the given question.
b = Base = 10
y = Log value = 4
Step 2: Put the values in the exponent antilog formula.
X = Antilogb(y) = by
= 104
= 10 x 10 x 10 x 10
X = 10000
Example 2
Find the antilog for base 2 and the exponent of antilog 9.
Solution
Step 1: Identify the base and log values.
b = Base = 2
y = Log value = 9
Step 2: Put the values in the antilog expression.
X = Antilogb(y) = by
= 29
= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
X = 512
Thus, to verify this antilog result use our above antilog calculator.
Important Antilog Values
Here are a few more examples in the below table for clarity of the antilog. Use our above antilogarithm calculator to verify the results.
| Questions | Expression | Answer |
|---|---|---|
| Antilog10(0) | 100 | 1 |
| Antilog10(1) | 101 | 10 |
| Antilog10(2) | 102 | 100 |
| Antilog10(3) | 103 | 1000 |
| Antilog10(4) | 104 | 10000 |
| Antilog10(10) | 1010 | 10000000000 |
| Antilog10(-2) | 10⁻² | 0.01 |
| Antilog10(-1) | 10⁻¹ | 0.1 |
| Antilog10(0.5) | 100.5 | 3.16 |
| Antilog10(1.5) | 101.5 | 31.62 |
| Antilog2(3) | 2³ | 8 |
| Antilog2(4) | 2⁴ | 16 |
| Antilog3(2) | 3² | 9 |
| Antilog4(1) | 4¹ | 4 |
| Antilog5(2) | 5² | 25 |
Note: If the base of any number is not given then conventionally, let the base be “10”. However, the antilog of “0” with any base is always equal to 1.
Frequently Asked Questions (FAQ’s)
How to calculate the antilog of a number?
To calculate the antilog manually: identify the base and log value and then put these values in the antilog expression “X = by” and simplify the results. Moreover, use the above antilog calculator to calculate the antilog value.
What is the Antilog of 3?
The antilog of the 3 depends on the base that is used in the logarithm function while the antilog value can be determined by the antilog expression “X = by”. For example, the antilog of 3 is “X = 103 = 1000” when the base of “10”. However, if the base is 2 then the antilog of 3 is “X = 23 = 8”.
What is Antilogarithm Table?
The Antilogarithm table is used to evaluate the antilog/anti-logarithm value to any number (either positive or negative number) by following some special process. In this process, splitting the characteristics and mantissa of logarithm value that is already found and viewing these values in the antilog table.
What is the difference between Log and Antilog?
A logarithm (log) is a mathematical function that finds the value exponential representation and determines the value only positive numbers but its results are either positive or negative. However, antilog (anti-logarithm) is the inverse of a log that undoes the process of logarithm and finds the value of both positive & negative numbers but the results are only positive numbers.
Can find the Antilog of Negative Numbers?
Yes, the antilog of any number is possible whether the number is positive or negative. Because antilog is known as the inverse of the logarithm and the results of the logarithm are positive or negative. Thus, the antilog of negative numbers can also be found.
