An inverse log calculator also known as antilog calculator is used to calculate the inverse logarithm of a number. Our antilog calculator calculates the antilog of any given number with any base. Enter the antilog value in the first input box and the antilog base in the second input box. Press the “Calculate” button to get the antilog of the given values. It will quickly calculate and publish the antilog result in front of you.
Antilog is a very important function in mathematics, and to understand it properly, let’s explore the topic in detail.
The logarithm is a function opposite to the exponentiation function. The logarithm of a certain y number equals to the exponent, and the base must be implemented to produce y to that exponent.
Logs have a base number raised to power and are used in different ways of expressing a number. Logs are important mathematical elements and are often used in mathematical equations, as below. Use our logarithm calculator to calculate Natural log online.
\(y = \log_bx\)
If we calculate the log of 64 with base 2 then, x will be 64 and b will be 2. After substituting the values in the log equation, it will become:
\(y = log_2 (64)\)
Change y as the power of the base 2, as written below:
2^y = 64
After simplifying further,
\(2^y = 2^6 \because y = 6\)
So, the log of 64 with base 2 is 6
To find the log of 650000 with base 10, substitute the x and b in the log equation.
\(b = 10, \text{and} x = 650000\)
The same equation will be used to calculate the log as in the previous example.
\(y = \log_b (x)\)
By putting the values in the equation, we get:
\(y = log_{10} (650000)\)
\(y = log (650000)\)
\(y \approx 5.81\).
So, the log of 650000 with base 10 will be 5.81. By using this method, you can calculate the log for any given number and base. These examples are only for demonstration purposes. For large and complex calculations, log and antilog functions are used in research institutes and laboratories.
What is an antilogarithm?
As the name suggests, antilog is the inverse of a logarithm. Antilog brings back the original value of a number that is obtained by taking the logarithm. Because logarithm is the inverse to exponentiation, it means antilog is exponentiation itself. After obtaining the logarithmic value of a number, antilog reverses the process and produces the original number.
Antilog of any number x can be calculated by raising the logarithmic base b on the both sides of the equation. It could be 10 or e, and it should be raised to the power of x.
\(y = \log_{b^{-1}}(x) = b^x\)
Log and antilog are inverse of each other which means that:
\(y = b^x = b^{log_by}\)
And
\(x = log_by = log_b(b^x)\)
Let’s calculate the inverse of log different numbers with examples to understand how it is calculated on paper.
Use this antilog equation \(y = b^x\) to evaluate the inverse log of any number with any base. If the base is 2, then it will be placed in the equation for b because b represents the base, and 5 should be raised as a power.
\(y = 2^5 \Rightarrow y = 32\)
To calculate the inverse of the log of 5 with base 10, suppose x = 5 and b = 10.
\(y = b^x \Rightarrow y = 10^5 \Rightarrow y = 100000\)
So the antilog of the 5 with base 10 is 100000.
Similarly, to calculate the antilog of 5 with base 20, substitute 20 in place of b in the equation.
\(y = b^x \Rightarrow y = 20^5 \Rightarrow y = 3200000\)
So the antilog of 5 with base 20 will be 3200000.
The same antilog equation y = bx will be used to calculate the antilog of any number with any base. If the base is 8, then it will be placed in the equation for b, and 10 should be raised as a power.
\(y = 108 \Rightarrow y = 100000000\)
To calculate the inverse of a log of 10 with base 10, x = 10, and b = 10.
\(y = bx \Rightarrow y = 1010 \Rightarrow y = 10000000000\).
So the antilog of the 10 with base 10 is 10000000000.
Similarly, to calculate the antilog of 10 with base 12, substitute 12 in place of b in the equation.
\(y = bx \Rightarrow y = 1012 \Rightarrow y = 1000000000000\)
So the antilog of 5 with base 20 will be 1000000000000.
To remove log or antilog from a number, you should evaluate either it is log or antilog. If it is a log, then use the antilog, and if it is an antilog, then use the log because both are the reverse functions of each other. An antilog on a log would remove the log, and a log on antilog will remove the antilog.
\(Log 6 = 0.7781512503836435\) with base \(10\)
And
Antilog \(0.7781512503836435 = 5.999\) which is approximately \(6\).
There is no antilog button on a calculator, but there is nothing to worry about. A numerical form of antilog can be used to calculate the inverse of the log. If there is no such thing in your calculator, you can use it by building it yourself by raising the antilog function to the base of the log.
How to convert logarithm to antilog?
It is easy to convert a log into an antilog. The base of the logarithm should be known. After writing down the base, raise the base the equation on both sides to the base. It will remove the log from the equation.
For example,
\(y = log^{10} (5) \Rightarrow 10^y = 5\)
The decimal part of a logarithm is called the mantissa. It is also known as significand. Our Sig Fig Calculator helps to count significant figures along with other important information about significant. Mantissa does not represent the magnitude because it is just the decimal part. It makes it easier for researchers to compare the results without considering the base.
For example:
in \(\log 5.93628, 0.93628\) is the mantissa. Or it can be described as the digits after the decimal value in a logarithmic value.
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