Antilogarithm is a mathematical approach that allows us to easily determine the inverse power of any integer. When performing computations, this phrase is crucial in determining the least and greatest quantities. In many mathematical problems, you have to find the 1/nth root of a specific number. If you made simple calculations to find it, then this will be time taking and maybe boring. By the concept of Antilog, we can easily convert all the numbers whether they are smaller or larger in a very precise way. In this article, we will study the concept of Anti-Logarithms with solved examples.

**What is Antilogarithm? **

The opposite way of taking logarithm is ‘Antilogarithm’. Categorically, given a logarithm of a number to a specific base, the antilogarithm is the exponent to which the base must be raised to obtain that number.

If b^{y} = z, **y** is the logarithm of **z** to the base **b**. The below is the mathematical form of this example.

**Log _{b}^{z} = y where b > 0 and b **

**≠ 1 also z > 0**

From Log _{b}^{z} = y we get b^{y} = z, by removing log and exponent interchange with the right-side value.

**Steps for Taking Antilogarithm**

To determine the anti-logarithm of a given number, we use an anti-logarithmic table.

Here are various methods for calculating the antilog.

**i.** The first step is to sort out the characteristic (part of the number before the decimal point) and the mantissa (part of the number after the decimal point) part of the given number.

**ii.** Finding a matching value for the mantissa using the antilog table is the second step. The row number was represented by the first two digits of the mantissa, and the column number by the third digit. Note its value.

**iii.** The table of antilog may also be including columns that impart the mean difference. Here for the same row of the mantissa, the column number in the mean difference is exactly equal to the digit in the fourth place. Write this value.

**iv.** Add the values to obtain the result.

You must include one in the characteristic. The decimal point should be placed at this value. After that many numbers to the left is where you place the decimal point.

**How to Calculate Antilogarithm Problems?**

We can solve the antilog problems either with the help of antilog calculator or antilog table.

**Example 1:**

Calculate antilog (3.3010)

**Solution:**

We can write it (by direct method)

Antilog (3.3010)=10^{3.3010}

= 10^{3+0.3010}

= 10^{3} · 10^{0.3010}

Antilog (3.3010) = 1000 · 2

**= 2000**

**Example 2: **

Solve for ‘t’ if A=2, B=3, C=5, D=10 in the following expression A+t^{B}=C+2D^{3}

**Solution: **

** Step 1:** The expression is

At^{B}=2CD^{3}

** Step 2:** Applying logarithm on both sides, we have

Log(At^{B})=Log(2CD^{3})

**∵ **Log (A×B)=Log A + Log B (Product law)

Log A + Log t^{B} = Log (2) + Log(C) + Log (D^{3})

Log t^{B}= 0.3010 + Log(C) + Log (D^{3}) − Log A

**∵ **Log (a^{n}) =n Log (a) (Exponent law)

B Log(t) = 0.3010 + Log(C) + 3 Log (D) − Log A

** Step 3:** Substituting values A=2, B=3, C=5, D=10 , we have

3 Log(t) = 0.3010 + Log (5) + 3 Log (10) – Log (2)

= 0.3010 + 0.6990 + 3(1) – 0.3010

3 Log (t) = 3.6990

Log (t) = 3.6990/3

Log (t) = 1.233

** Step 4:** Logarithm will convert into Antilog moving towards the right,

t = Antilog (1.233)

**t=17.1 **

**Example 3:**

Find the Antilogarithm of the number 6.0098 by using the calculator.

**Solution:**

Since the given number is 6.0098, so we take 10^6.0098 = 1,022,821.86

**Antilog (6.0098) = 1,022,821.86**

**Applications of Antilogarithm:**

**1. In Physical Phenomenon:**

We can’t overstate the importance of logarithms and antilogarithms in many physical phenomena such as earthquake magnitude. In this phenomenon, we utilize the method of logarithm and antilog to determine the Richter scale magnitude of earthquakes. Additionally, we also consider the concepts of logarithm and antilog to compute the sound intensity level. We can use the following formula to calculate the sound intensity level.

**Sound intensity level=10 log I/I _{O}**

** L – L _{O}= **

**10 log I/I**

_{O}**2. In Chemistry:**

In many chemical reactions, we use the concept of logarithms and antilog in finding the pH (to check whether the substance is acidic or basic).

pH = log10 [H^{+}]

Similar to this, we can employ a variety of catalyst types to expedite the chemical reaction. We can determine the reaction’s speed from the amount of catalyst present. The speed is obtained using an antilogarithm to examine the catalyst’s effect. For using the least or the most quantity of catalyst, we must keep in mind the concepts of antilog and logarithm.

**3. In Finance:**

To depict two similar price changes by the same vertical changes on the scale, many well-known logarithmic pricing scales are employed in chart plotting. We appreciate the analysis of price fluctuations by using this.

**4. In Engineering:**

The idea of antilog is frequently employed in this discipline, including the technical engineering. In this, engineers test the dependability of a certain tool or machine using several numerical precisions at numerous time intervals.

**5. In Biology:**

Biomedical engineers employ antilog techniques and concepts to evaluate the impact of light intensity on bones. They also use these concepts to determine the time between cell development and death, and prevent UV exposure.

**6. In the Number Precisions:**

When numbers are too big or too small to grasp comfortably, it is frequently employed. Without employing the concepts of logarithm and antilog, it is challenging to quickly discover a solution to many computations that are either too large or too little, just like in astronomy.

**Conclusion**

In the above discussion, we have learned about the concept of Antilog and its importance. By understanding the basic steps, we can easily sort out all the problems relevant to extreme values. By solving its example step by step, you can easily resolve its everyday examples. Through knowing its importance in different aspects of life, like physical sciences, engineering, computer technology, mathematics, and business as well we can say that Antilogarithm is a unique and very helpful concept in this regard.