Antilog Calculator

Antilog Calculator

Our online inverse log calculator calculates the reverse value of a log by using a given number and a base. Values generated by using the log function can be reversed in their previous state by using this antilog calculator. This calculator makes the process of antilog calculation very simple. Follow these steps to calculate the antilog of a number using this best antilog calculator.

• Enter the log value in the text box labeled as log number.
• Enter the base value in the text box labeled as a log base. The base should be a positive number.
• Click on the “Calculate” button to calculate the antilog for the given values.
• It will calculate the antilog of the number with a given base in the blink of an eye.
• It can generate two random numbers for log value and base value for simulation.
• Click on the “Generate random number” button to generate the random number and click “Calculate” to see the result.

What is Logarithm?

A logarithm is the exponentiation’s inverse function. A logarithm is an exponent to which a given base has to be multiplied to itself. In order to reach a given number, logarithm tracks the number of times the same factor must be multiplied to itself. It is the inverse component of exponentiation in which it is written as bn if represented as a math operation. The base b is multiplied to itself n number of times.

The log was developed by Scottish physicist and mathematician John Napier, in the 16th century as a measurement tool. The Greek word logos means ratio, and arithmos means numbers were used by Napier to term logarithm. It means the ratio number when combined together.

Types of Logarithms

There are two types of logarithm, common and natural logarithm.

• If there is no base specified to evaluate log, then it will be referred as a common log. It uses the base 10 for the calculations. For example, log (50). In this example, no base is given. So, we calculate the log using base 10.
• If the base is e, which is a constant in mathematics, it will be referred as a natural logarithm. The value of e is approximately 2.718281828459 and will be written as log_e(x).

How to calculate log?

When the calculations go beyond simplicity, it becomes a very complicated and struggling task. Regardless of it's a number, population growth, or wide distances, the logarithm can make life easier. It can make it easier to understand large sums, including lengthy and complicated calculations.

Below is the standard equation used for log function.
log_b (x) = y

In this equation, b is the base which is multiplied to itself while y is the logarithm, which is the number of times it is multiplied and x the number which is given to calculate log.

Let’s understand the concept of the log by some examples.

Log of 16 with base 2

If we calculate the log of 16 with base 2 then,

x = 16 and b = 2

So, we can write it as:

log₂ (16) = y

Or

y = log₂ (16)

Now, raise the y as the power of the base, it will become:

2^{y =} 16

By further simplifying we get,

2^{y =} 2⁴  è  y = 4

So, the log of 16 with base 2 is 4. It can be easily deduced that log tells how many times a number is multiplied to itself to reach a certain number. We use that certain number to calculate that “how many times,” which is done by log function.

Log of 800000 with base 10

Let’s find the log of 800000, which is a greater number than in the previous example, with base 10. So,

b = 10, and x = 800000

The equation will be the same to calculate the log for any value.

y = log_b (x)

By substituting the values in the equation, we get:
y = log₁₀ (800000)
y = log (800000)

y = 5.90 approx.

So, the log of 800000 with base 10 will be 5.90. Similarly, the log can be calculated for any number and any base as well by using this method.

What is antilog?

Antilog is a mathematical function inverse of log and used to reverse the operation of log on a number. A number that is evaluated by using a log can be returned to the original one by applying antilog on it. The below equation represents the antilog and used to calculate the antilog for a given number.

y = log_b^-1(x) = b^x

How to calculate antilog?

Logarithm base b must be raised to calculate the antilog of a number. The base is mostly 10 or a constant e (2.718281828459), which should be raised to the power that will produce the number.

Antilog of 6 with base 3, 8 and 10

Use this antilog equation y = b^x to calculate the log inverse of a number with a specific base. If the base is 3, then it will be placed in the equation for b because b represents the base, and 6 should be raised as a power.

y = 3⁶ will become y = 729

To calculate the antilog of 6 with base 8, 6 will be placed as x, and 8 will be used as b.

y = b^x

y = 8⁶

y = 262144

So the antilog of the 6 with base 8 is 262144.

To calculate the antilog of 6 with base 10, put 10 in place of b in the equation.

y = b^x

y = 10⁶

y = 1000000

So the antilog of 6 with base 10 will be 1000000.

Antilog of 2 with different bases

First, let’s calculate the antilog of 2 with the same base 2. If the base is 2, then it will be placed in the equation for b, and 2 should be raised as a power.

y = 2²

y = 4

The antilog of 2 with the base 2 is 4.

To calculate the inverse of a log of 2 with base 10, substitute x = 2, and b = 10.

y = b^x

y = 10²

y = 100.

So the antilog of the 2 with base 10 is 100.

To calculate the antilog of 2 with base 5, substitute 12 in place of b in the equation.

y = b^x

y = 5²

y = 25

So the antilog of 2 with base 5 will be 25.

All the above examples show that the antilog calculates the value by multiplying the base with itself by the x number of times. In simple words, antilog of 2 with base 3 would be 3 x 3 = 9. We will multiply three with three 2 times because 2 will be raised as a power to the base 3.

Applications of log and antilog

Log and antilog are used to calculate large amounts and data that cannot be calculated easily. The exponential function works as a time saver because it can do calculations of billions very quickly. It facilitates computing and facilitates understanding of calculations. It also eliminates the chances of error.

If we have an exponential function, we can find a logarithmic function immediately. Given that the antilogarithmic function is the exponential function, the antilogarithmic applications are exponential applications. That is why exponential functions are very useful. Logarithms are used in an exponential decay, compound interest, and model population growth.

The log function is used for objective measurements to compute the natural phenomenon such as the brightness of different objects, strength of earthquakes, and windstorm force. It is also used in calculating the economic growth rates if used in finance. Log and antilog are used in Music, Acoustics, Chemistry, Statistics, Mathematics, and many other fields where measurements are in a large amount, need accuracy, and very difficult to handle.