Sometimes calculating a logarithm can be challenging, especially when the numbers are not compatible with the base of the logarithmic function. That's where the change of base formula calculator comes in to make things easier for you.
This tool helps you to convert logarithms from one base to another and make calculations more manageable when working with logarithms in different bases.
“In mathematics, the logarithm is the inverse operation of exponentiation.”
The logarithm is also called a log, it tells you the power (exponent) to which a base needs to be raised in order to equal a given number.
To change the base of a logarithm, you can use the change of base formula. The formula is as follows:
\(\log_b a = \frac{\log_c a}{\log_c b}\)
Where
So, to change the base from (b) to (c), you have to take the logarithm of (a) to the base (c) and divide it by the logarithm of (b) to the base (c).
Here is a step-by-step procedure:
Suppose we want to find the value of (\log_4 32) using the change of base formula. Here’s how we do it step by step:
So, \(\log_4 32 \approx 2.5\), you can also calculate this by using this change of base formula calculator provided by Calculatored.
Original Logarithm | New Base | Change of Base Formula | Solution |
---|---|---|---|
\(log_3(8)\) | 5 | \(log_5(8) = log_3(8) / log_3(5)\) | ≈ 4.28 |
\(log_2(16)\) | 10 | \(log_10(16) = log_2(16) / log_2(10)\) | 4 |
\(ln(4)\) | 3 | \(log_3(4) = ln(4) / ln(3)\) | ≈ 1.26 |
\(log_e(2)\) | 2 | \(log_2(e) = log_e(2) / log_e(2)\) | 1 |
A change of base refers to the process of converting a logarithm from one base to another using a specific formula called the "Change of Base Formula.
Keep in touch
Contact Us© Copyright 2025 by calculatored.com