What is a Logarithm?

A logarithm serves as the opposite action to exponentiation. It addresses the inquiry, “What exponent must be applied to a base to yield a specific number?” It is expressed in this manner:

• Loga b = n
• a = base
• b = value
• n = exponent

How to use the logarithm calculator?

This free MathCalc logarithm calculator allows you to find the log of a number with any base, use the common log (base 10), binary log (base 2), the natural log (base e), or a custom base. You can also convert between logarithmic and exponential forms.

Choose to Calculate Common Log (Base 10)

Find log₁₀(1000)

• Step 1: Calculating the logarithm of 1000
• Step 2: Common logarithm (base 10): log₁₀(1000) = 3

Result: log₁₀(1000) = 3

Choose to Calculate Natural Log (Base e)

Calculate ln(24)

• Put the 24 in the number bar values
• Select Natural Log (Base e)
• Custom base is disabled here.
• Click on calculate, and you see the results in seconds.
• Step 1: Calculating the logarithm of 24
• Step 2: Natural logarithm (base e): ln(24) = 3.1780538303479

Result: ln(24) = 3.178054

Choose to Calculate Binary Log (Base 2)

Calculate log₂(25)

• Put the 25 in the number bar values
• Select Binary Log (Base 2)
• Custom base is disabled here.
• Click on calculate, and you see the results in seconds.
• Step 1: Calculating the logarithm of 25
• Step 2: Binary logarithm (base 2): log₂(25) = 4.6438561897747

Result: log₂(25) = 4.643856

Choose to Calculate the Custom Base

Calculate log₅(25)

• Put the 25 in the number bar values
• Select Custom base
• Put 5 in the custom base bar value.
• Click on calculate, and you see the results in seconds.
• Step 1: Calculating the logarithm of 25
• Step 2: Custom logarithm (base 5): log₅(25) = 2

Result: log₅(25) = 2

Why use the MathCalc calculator?

Get Quick Results

Finding the log by hand can take time and effort, especially when dealing with decimal values. No need for manual calculation and log tables. This free calculator gives accurate results in seconds. Example: Finding log (1000) by hand can take time; the calculator instantly shows the result as 3.

Remove the Risk of Human Error

When you do math by hand, you could make small mistakes that could cost you money. The tool uses formulas that have been proven to work throughout time, so your results will always be correct. Use the MathCalc Logarithm calculator to make sure your calculations are accurate.

Great for Everyone

This free calculator is helpful for students, teachers, or anyone who is having trouble with logarithms.

Tips for Getting the Most Remarkable Results:

• Don't type in negative numbers because the log of negative values doesn't exist in absolute numbers.
• Always check your input twice.
• Don't use any special characters.

FAQs

What is the use of a logarithm?

In arithmetic, logarithms are used to reverse an exponentiation. They are helpful in equations related to sound levels, exponential growth, and so on.

What is the log of 1 in any base?

The log of 1 is always 0 because 0 raised to any base equals 1.

Can this calculator be used for natural logs?

Yes! To use the base e, choose "Natural Log" (In).