Log Calculator is a tool created for calculating the values of logarithms in various bases such as e, 10, or others. Here, you need to enter the input for which you want to find the logarithm value and specify the base of the logarithm.
How to Use Log Calculator?
To use Log Calculator you can use the following steps:
Step 1: Enter the number for which you want to find the logarithm into the "Enter Number" input.
Step 2: Enter the base of the logarithm in the "Enter Base" input.
Step 3: Click on "Calculate".
Step 4: Interpret the result based on your requirements.
Step 5: Repeat the process for additional calculations if necessary.
What is 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 log5(125).
- Find the value of log3(81).
- Calculate the logarithm of 0.01 with base 10.
- Determine the natural logarithm of e5.
- Compute log12(144).
- Find the value of log7(49)
- Calculate the logarithm of 27 with base 3.
Conclusion
In conclusion, the Log Calculator is an essential tool for handling logarithmic computations effectively and precisely. It serves professionals in engineering, finance, and scientific research, as well as students learning mathematical concepts, by simplifying complex operations with its user-friendly interface and accurate results.
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