Negative Log Calculator

Welcome to the Omni's negative log calculator. Using this calculator, you can find the negative logarithm of any number with any chosen base. For details on logarithms and how to find the negative log of a number, read the description given below.

Do you know how many 2's you have to multiply together to get 8?

The answer is easy; 2³ = 8, i.e., you have to multiply three 2's together to get 8.

But what if we ask you to calculate the number of 7's you need to multiply to get 5,764,801? Not so easy anymore, right?

Thanks to the Scottish mathematician John Napier, who invented logarithms as a calculation tool in the 16th century, we can handle numerical expressions that involve multiplications or divisions of large numbers.

Logarithms are extensively used in chemistry, physics, mathematics, and engineering problems to solve complex calculations with ease.

Before going any further, let's try to understand what a logarithm is!

For any positive real number a, and any rational number n, let aⁿ = b
where b is also a real number.

We can say that the n-th power of base a is b or that we need to multiply a by itself n times to get b. We can also say that the logarithm of b to base a is n and express this mathematically as:

$\log_a(b) = n$

To understand this with an example, let us come back to our first problem.

We know that 2³ = 8,
i.e., $\log_2(8) = 3$. Hence, we can say that the logarithm of 8 to base 2 is 3.

You must have realized by now that 3 is the exponent of 2. Therefore, while calculating the logarithm of a number, we are simply trying to determine the exponent to which the base must be raised to get that number.

To find the answer to our second problem, you can use our log calculator. You can also check our antilog calculator to find the antilog of any number.

To calculate the negative logarithm of a number, we need to determine how many times we should divide 1 by the base to get that number, i.e.,

$-\log_a(b) = n$

$\log_a(1/b) = n$

or

$1/a^n = b$

Negative logarithms are frequently used in analytical chemistry to determine the pH of aqueous solutions.

Also, remember that the negative logarithm of a number and logarithm of a negative number is not the same thing, i.e.,

$-\log_a(b) ≠ \log_a(-b)$

The logarithm of a negative real number is not defined. For details on finding the logarithm of complex numbers, you can refer to this github post.

To demonstrate how to find the negative log of any number using our online negative log calculator, let us calculate the value of $-\log_2(8)$ :

1. Enter the number you want to calculate the negative logarithm of, i.e., 8, in the first row.
2. Enter the base, i.e., 2, in the second row.
3. If you want to calculate the natural log, use e as the base.
4. The negative log value, i.e., -3, appears in the last row.