What is the use of antilogarithm?

To retrieve the original number from a given logarithmic value.

What is the base of antilog?

Commonly, base 10 is used, especially in scientific and engineering calculations.

How do I calculate antilog without a calculator?

Use a printed antilogarithm table PDF and apply the formula using characteristic and mantissa.

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Antilogarithm

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Antilogarithm

Antilogarithm is the inverse operation of a logarithm, used to find the original number from its logarithmic value. If $lo g_{b} x = y$ , then $x = b^{y}$ is the antilogarithm of y. It plays a key role in scientific calculations, exponential growth models, and competitive exams. Understanding logarithm and antilogarithm concepts simplifies complex multiplications and helps in accurate data interpretation across physics, chemistry, engineering, and finance.

1.0Antilogarithm Meaning

The antilogarithm (often written as antilog) of a number is the inverse operation of a logarithm.

If:

$lo g_{b} x = y$

Then:

$x = b^{y}$

Here, x is the antilogarithm of y to the base b.

So, in simpler terms:

Antilogarithm tells us what number was originally taken to get a given logarithm.

2.0Antilogarithm Formula

To find the antilogarithm, use this formula:

$Antilog_{b} (y) = b^{y}$

Where:

b is the base of the logarithm (usually 10 or e)
y is the logarithmic value
$b^{y}$ gives the original number (antilog)

3.0How to Calculate Antilogarithm

There are three main ways to calculate an antilogarithm:

1. Using the Formula

$Antilog_{10} (2.3010) = 1 0^{2.3010} \approx 200$

2. Using a Scientific Calculator

Enter the log value, press the "SHIFT" or "2nd" key, then press the "log" key to get the antilog.

3. Using an Antilogarithm Table

Split the number into its characteristic (integer part) and mantissa (decimal part).
Use the antilogarithm table PDF to find the value corresponding to the mantissa.
Multiply by $1 0^{characteristic}$ to get the result.

4.0Rules of Antilogarithm

Here are some important rules and properties:

Inverse of Logarithm:

$Antilog_{b} (lo g_{b} (x)) = x$

Antilog of Sum:

$Antilog (a + b) = Antilog (a) \times Antilog (b)$

Antilog of Difference:

$Antilog (a - b) = \frac{Antilog ( a )}{Antilog ( b )}$

Base 10 Antilog:

Commonly used base in logarithmic tables and competitive exams is 10.

5.0Antilogarithm Examples

Example 1: Find the antilog of 2.3010

Solution:

$Antilog (2.3010) = 1 0^{2.3010} \approx 200$

Example 2:

If $lo g_{10} x = - 1.523$ , find x

Solution:

$x = 1 0^{- 1.523} \approx 0.030$

Example 3:

Solution:

Use antilog table to find antilog of 0.4771

Mantissa = 0.4771
From table: antilog(0.4771) ≈ 3
Hence, $Antilog (0.4771) \approx 3$

6.0Applications of Antilogarithms in Science

Physics: To compute values in decibel scales, exponential growth/decay, and wave intensity.
Chemistry: In pH calculations and reaction rates.
Biology: Population modeling and genetics.
Engineering: In calculations involving logarithmic amplifiers and signal processing.
Astronomy & Earth Sciences: Earthquake magnitude (Richter scale), star luminosity.

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Antilogarithm

Antilogarithm is the inverse operation of a logarithm, used to find the original number from its logarithmic value. If $lo g_{b} x = y$ , then $x = b^{y}$ is the antilogarithm of y. It plays a key role in scientific calculations, exponential growth models, and competitive exams. Understanding logarithm and antilogarithm concepts simplifies complex multiplications and helps in accurate data interpretation across physics, chemistry, engineering, and finance.

1.0Antilogarithm Meaning

The antilogarithm (often written as antilog) of a number is the inverse operation of a logarithm.

If:

$lo g_{b} x = y$

Then:

$x = b^{y}$

Here, x is the antilogarithm of y to the base b.

So, in simpler terms:

Antilogarithm tells us what number was originally taken to get a given logarithm.

2.0Antilogarithm Formula

To find the antilogarithm, use this formula:

$Antilog_{b} (y) = b^{y}$

Where:

b is the base of the logarithm (usually 10 or e)
y is the logarithmic value
$b^{y}$ gives the original number (antilog)

3.0How to Calculate Antilogarithm

There are three main ways to calculate an antilogarithm:

1. Using the Formula

$Antilog_{10} (2.3010) = 1 0^{2.3010} \approx 200$

2. Using a Scientific Calculator

Enter the log value, press the "SHIFT" or "2nd" key, then press the "log" key to get the antilog.

3. Using an Antilogarithm Table

Split the number into its characteristic (integer part) and mantissa (decimal part).
Use the antilogarithm table PDF to find the value corresponding to the mantissa.
Multiply by $1 0^{characteristic}$ to get the result.

4.0Rules of Antilogarithm

Here are some important rules and properties:

Inverse of Logarithm:

$Antilog_{b} (lo g_{b} (x)) = x$

Antilog of Sum:

$Antilog (a + b) = Antilog (a) \times Antilog (b)$

Antilog of Difference:

$Antilog (a - b) = \frac{Antilog ( a )}{Antilog ( b )}$

Base 10 Antilog:

Commonly used base in logarithmic tables and competitive exams is 10.

5.0Antilogarithm Examples

Example 1: Find the antilog of 2.3010

Solution:

$Antilog (2.3010) = 1 0^{2.3010} \approx 200$

Example 2:

If $lo g_{10} x = - 1.523$ , find x

Solution:

$x = 1 0^{- 1.523} \approx 0.030$

Example 3:

Solution:

Use antilog table to find antilog of 0.4771

Mantissa = 0.4771
From table: antilog(0.4771) ≈ 3
Hence, $Antilog (0.4771) \approx 3$

6.0Applications of Antilogarithms in Science

Physics: To compute values in decibel scales, exponential growth/decay, and wave intensity.
Chemistry: In pH calculations and reaction rates.
Biology: Population modeling and genetics.
Engineering: In calculations involving logarithmic amplifiers and signal processing.
Astronomy & Earth Sciences: Earthquake magnitude (Richter scale), star luminosity.

Frequently Asked Questions

What is the use of antilogarithm?

What is the base of antilog?

How do I calculate antilog without a calculator?

Frequently Asked Questions

What is the use of antilogarithm?

What is the base of antilog?

How do I calculate antilog without a calculator?

Join ALLEN!

Antilogarithm

1.0Antilogarithm Meaning

2.0Antilogarithm Formula

3.0How to Calculate Antilogarithm

4.0Rules of Antilogarithm

5.0Antilogarithm Examples

6.0Applications of Antilogarithms in Science

Table of Contents

Join ALLEN!

Antilogarithm

1.0Antilogarithm Meaning

2.0Antilogarithm Formula

3.0How to Calculate Antilogarithm

4.0Rules of Antilogarithm

5.0Antilogarithm Examples

6.0Applications of Antilogarithms in Science

Table of Contents