# log calculator

Choose to calculate:
Log bn

#### RESULTS

Log
--

Our logarithm calculator determines the logarithmic value of a number given that you provide the log base. When the log base is provided for, you can calculate the natural log, common log and binary log values. Its just a matter of choosing. This log equation solver is a free to use tool to facilitate mathematicians, engineers, physicists and students in particular.

## What is logarithm?

In Math, the log is the reverse function of exponentiation. What this implies is that the log of a given number, say x, is exponent to which another static number, the base (say b), must be elevated, to reproduce the number x.

In the simplest case, the log sums the number of occurrences of the same factor in repetitive multiplication; e.g., since 10000 = 10 × 10 × 10 × 10 = 104, the "logarithm to base 10" of 10000 is 4. The log of x to base b is represented as log b (x). This is how you can write a log.

## Log rules, Formulas and Proofs

### Product Rule Law:

#### formula

$$\log_a(MN) = \log_a M + \log_a N$$

#### Proof

$$\mathbf{Let:} \log_a M = x \Rightarrow \mathrm{sup} > x = M$$ $$\mathbf{and} N = y \Rightarrow a^y = N$$

$$\mathbf{Now} a^x \times a^y = MN \mathbf{or}, a^{x + y} = MN$$

Therefore from definition, we have,

loga (MN) = x + y = loga M + loga N [putting the values of x and y]

Corollary: The law is true for more than two positive factors i.e.,

loga (MNP) = loga M + loga N + loga P

since, loga (MNP) = 1oga (MN) + loga P = loga M+ loga N+ loga P

Therefore in general, loga (MNP ….... )= loga M + loga N + loga P + ……. .

Hence, the logarithm of the product of two or more positive factors to any positive base other than 1 is equal to the sum of the logarithms of the factors to the same base.

## How to calculate log with our calculator

This log base calculator is ours is exceptionally easy to use. You have to follow very simple steps to do the calculation. The user-interface of this ln calculator ensures that even this is not necessary but we will list the steps just in case.

• First, choose the log you want to calculate, for instance: natural log, common log, binary log or custom log.
• Second, input the base value.
• Third, press ‘calculate’

Calculator Widget

Add Log Calculator to your website and allow your users to use this calculator directly from your website. This widget is 100% free for all users, You can add it on multiple websites.

Related Calculators
User Ratings
• Total Reviews 1
• Overall Rating 5/5
• Stars
Reviews