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Enter a number and its base and the smart log calculator aids in determining the log, natural log, and anti-log, with calculations shown.

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Yes – this is a smart log calculator that helps to compute logs and inverse log of any number base. So, let’s begin with the term of ‘Logarithm.’

In mathematical term, the logarithm (log) operation is said to be as the inverse to exponentiation, means the (log of a number) is the exponent to which another fixed number known as ‘base’ was raised to generate the number. However, you can do any logarithm calculations by using the logarithm calculator. More specifically, the logarithm of a number x according to base b is the exponent to which b has to be raised to produce x. In few words, the logarithm of y to base b is the solution y of the given equation:

= x

And for any x and b, there is:

x =

**Logarithm product rule:**

(x*y) = (x) + (y)

**Logarithm quotient rule:**

(x/y) = (x) - (y)

**Logarithm power rule:**

) = y*(x)

**Logarithm base switch rule:**

(c) = 1/(b)

**Logarithm base change rule:**

(x) = (x)/ (b)

- Common Logarithm – this logarithm has a base of 10 (b=10), it has many uses in engineering, navigation, many of the sciences like physics and chemistry. People that belongs to field of sciences or engineering often uses log base calculator to perform log base calculations
- Natural Logarithm – this logarithm has a base of the number e (the Euler number, 2.71828), it is often used in physics and math due to its simpler derivative, students often use natural log calculator to do math’s of the natural log
- Binary Logarithm – this logarithm has a base of 2, you can compute log2 calculations with the help of log base 2 calculator, this log2 widely used in computer science such as for representing data units

When using the above logarithmic calculator you just have to enter a ‘base’ of 10 for the common logarithm, 2 for the binary logarithm, and leave the base field empty to compute the natural logarithm.

The log form or log calculator is a significant tool that helps to calculate any type of logarithm of a real number of any base you want. In simple words, this quality tool works as a log solver to understand how to solve logarithms of any number. Also, you can be able to calculate the inverse of log using this inverse log calculator for the real number with respect to the given or natural base values.

- First of all, you have to select the ‘Log’ option from the drop-down menu
- Then, you have to enter the number in the designated field
- Right after, you have to enter the number base into the given field
- Finally, hit the calculate button of this logarithms calculator to get your results

- Here first you have to select the ‘Antilog’ option from the drop-down menu
- Then, you have to enter the number in the given field
- Very next, you have to enter the number base into the designated field
- Once done, click the calculate button of antilog calculator to get inverse log value

Note: This expanding logarithms calculator works efficiently to find the logarithm or antilogarithm of any number according to the given base.

Keep in mind, exponents are known as just the inverse function of logarithm, and logarithms are said to be as the inverse function of exponents. With this, it is clear that the Inverse log or Antilog is just another term for exponents. Therefore, logarithms are another way to conceive of exponents. If you have an idea about 8 to the second power, or 8 square equals 64, then it can represent that as: 8^2 = 64.

The ‘Log’ function on a scientific or graphing/scientific calculator is a key that allows the user to perform logarithms calculation. Logarithms are ways that assist to determine what exponents you need to multiply into a specific number. Typically, the log function on most calculators works in the same way!

You have to express terms into common logarithms, the relationship is represented by log mn = log m + log n.

For Example:

The expression is 100 × 1,000:

However, it can be calculated by looking up the logarithms of 100 (2) and 1,000 (3), then you ought to add the logarithms together (5), right after there is a need to look at its antilogarithm (100,000) in the table.

Let’s suppose that there is a need to calculate log2 of the number “12” that is log2 (12). To calculate the base 2 logarithm of a number (y), you have to divide the common log of y by the common log of 2.

In Mathematical term, log10(x) is equivalent to log (10, x). The logarithm with the base (10) is expressed for all complex arguments x ≠ 0. log10(x) , here is need to rewrites logarithms to the base 10 in the mathematical terms of the natural logarithm i:e log10(x) = ln(x)/ln(10) .

According to the term of a logarithm, then antilog is said to be as the inverse function of a logarithm – so log(b) x = y. You can write this with exponential notation such that antilog (b) y = x implies = x.

For example:

If log 39.2 = 1.5933, then the antilog 1.5933 = 39.2

- First, you have to note the base of your logarithm
- Very next, you ought to raise both sides of the equation to that base, this removes the log – For e:g, y = log 15(8) becomes 15y = 8
- And, solve the remaining equation

Let’s take a look!

- If the logarithmic expression log4(⅛) = -3, then the equivalent exponential form is 1/8 = 4^-3
- If the logarithmic expression log4(28) = 3, then the equivalent exponential form is 28 = 4^3
- If the logarithmic expression log38(7) = 1/2, then the equivalent exponential form is 6 = 38^1/2
- If the logarithmic expression log6(2) = 1/3, then the equivalent exponential form is 1/6 = 2^-3

If you want to determine a log using an arbitrary base, then you have to stick on the following rules:

logₐ(x) = ln(x) / ln(a)

logₐ(x) = lg(x) / lg(a)

Apart from it can use the above log base 10 calculator or natural log calculator to calculate it!

The logarithmic equation calculator will be taken into account for understanding (K-12 education) queries or to understand the concept of exponents and logs. Also, you can utilize this tool calculus, algebra, probability and many other fields of science and life.

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