Log Calculator (original) (raw)
Last Updated : 18 Mar, 2026
Log Calculator is a tool created for calculating the values of logarithms in various bases such as e, 10, or others.
Steps to Use Log Calculator
To use Log Calculator you can use the following steps:.
**Step 1: Enter the base of the logarithm in the “Base (b)” input field, or choose a preset base such as Base 10, Base 2, or Custom Base.
**Step 2: Enter the number for which you want to calculate the logarithm in the “Enter Value” input field
**Step 3: Click on the “Calculate” button.
**Step 4: View and interpret the calculated logarithmic result displayed on the screen.
**Step 5: Repeat the process with different values if additional calculations are required.
Logarithm
- Logarithm is a mathematical function that determines the exponent or power to which a fixed number, known as the base, must be raised to produce a given number.
- In other words, it represents the inverse operation of exponentiation. Logarithms are denoted by the notation "log" followed by a subscript indicating the base of the logarithm.
Logarithm Definition
The logarithm of a number "x" with base "b" is expressed as follows:
logb(x) = y
Here, "x" is the given number, "b" is the base, and "y" is the exponent or power to which "b" must be raised to obtain "x".
For example, if we have log2(8) = 3, it means that 2 raised to the power of 3 equals 8.
Log Table
Log table, short for logarithm table, is a reference tool used in mathematics and various scientific disciplines which helps students and other professional in their logarithmic calculations. Log tables generally list the logarithms of numbers with various bases, such as common logarithms (base 10) or natural logarithms (base e).
Read more about Log Table.
Values of Loge or ln
Natural logarithm is logrithm with a base of eular's number i.e., "e ≈ 2.71828". Provided below are examples of frequently observed values for the natural logarithm:
| Number | Natural Logarithm (loge or ln) |
|---|---|
| 1 | 0 |
| 2 | 0.693147 |
| e | 1 |
| 3 | 1.098612 |
| 4 | 1.386294 |
| 5 | 1.609438 |
| 6 | 1.791759 |
| 7 | 1.945910 |
| 8 | 2.079442 |
| 9 | 2.197225 |
| 10 | 2.302585 |
Values of log10
Logarithm base 10, also known as the common logarithm, derives its name from having a base of 10. Below are some common values of the base 10 logarithm:
| Number | Common Logarithm (log base 10) |
|---|---|
| 1 | 0 |
| 2 | 0.301 |
| 3 | 0.477 |
| 4 | 0.602 |
| 5 | 0.699 |
| 6 | 0.778 |
| 7 | 0.845 |
| 8 | 0.903 |
| 9 | 0.954 |
| 10 | 1 |
Log Vs Antilog
Logarithm and antilogarithm are mathematical concepts that are closely related but serve opposite purposes. In simple words, logarithms transform numbers into exponents, whereas antilogarithms reverse this process, converting exponents back into their original numbers.
| Number (x) | Logarithm (log10(x)) | Antilogarithm (10x) |
|---|---|---|
| 1 | 0 | 10 = 10 |
| 10 | 1 | 1010 = 10,000,000,000 |
| 100 | 2 | 10100 |
| 1000 | 3 | 101000 |
| 10000 | 4 | 1010000 |
| 0.1 | -1 | 10-1 = 0.1 |
| 0.01 | -2 | 10-2 = 0.01 |
| 0.001 | -3 | 10-3 = 0.001 |
| 0.0001 | -4 | 10-4 = 0.0001 |
Unsolved Practice Problems - Log Calculator
- Find the logarithm of 64 with base 2.
- Calculate the natural logarithm of 20.
- Determine the logarithm of 1000 with base 10.
- Compute log 5 (125).
- Find the value of log 3 (81).
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