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Maths

Log Calulator [With Steps]

Table of Contents

Calculate logarithms using Wiingy’s single logarithm calculator. Please provide any two values to calculate the third value using the logarithm equation,
logbx=y (b=logarithmic base)

Find Log of

with base value

Antilog

Logarithm Value of 10 with base e = 2.302585092994046

What is Logarithm?

In Mathematics, logarithm or log is the inverse function to exponentiation. In simple terms, the logarithm is the power to which the given number needs to be raised in order to obtain another number. That means that the logarithm of a given number x is the exponent to which another fixed number, the base, must be raised in order to produce that number x.

Logarithms are used to solve problems involving exponential growth or decay.

Let’s understand the concept with an example.

For example,
If b=10
then, then the logarithm of 1000 to base 10 is 3
because 10 to the power of 3 is 1000 (10^3 = 1000).

The logarithm function is written as log_b(x), or sometimes as just log(x) when the base is understood. The logarithm of x to base b is denoted as log_b(x).

What are the 7 Rules of Logarithms?

There are 7 rules of logarithms to keep in mind.

  1. The exponent to which the base must be raised in order to obtain a number is determined by the logarithm of the number to the given base. For example, log_2(8) = 3 because 2^3 = 8.
  2. The opposite of exponentiation with a specific base is a number’s logarithm to that base. That means that if b is the base, then log_b(x) is the exponent to which b must be raised to produce x, and b^(log_b(x)) = x.
  3. The exponent to which the base must be raised in order to obtain a number is determined by the logarithm of the number to the given base. For example, log_2(8) = 3 because 2^3 = 8.
  4. The logarithm of a product is the sum of the logarithms of the factors. For example, log_2(4*8) = log_2(4) + log_2(8) = 2 + 3 = 5.
  5. A quotient’s logarithm is equal to the numerator’s logarithm minus the denominator’s logarithm. For example, log_2(8/4) = log_2(8) – log_2(4) = 3 – 2 = 1.
  6. The logarithm of a power is derived by multiplying it by the base’s logarithm. For example, log_2(8^3) = 3log_2(8) = 33 = 9.
  7. Regardless of the base, the logarithm of 1 is always 0.