# Definition of logarithmic

## What is the basic definition of logarithm?

logarithm,

**the exponent or power to which a base must be raised to yield a given number**. Expressed mathematically, x is the logarithm of n to the base b if b^{x}= n, in which case one writes x = log_{b}n. For example, 2^{3}= 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log_{2}8.## Why is it called logarithmic?

**Napier coined the term for logarithm in Middle Latin, “logarithmus,” derived from the Greek, literally meaning, “ratio-number,” from logos “proportion, ratio, word” + arithmos “number”**. The common logarithm of a number is the index of that power of ten which equals the number.

## What is use of logarithmic?

In Mathematics, before the discovery of calculus, many Math scholars used logarithms

**to change multiplication and division problems into addition and subtraction problems**. In Logarithms, the power is raised to some numbers (usually, base number) to get some other number.## What is logarithmic function example?

For example,

**y = log2 8**can be rewritten as 2y = 8. Since 8 = 23 , we get y = 3. As mentioned in the beginning of this lesson, y represents the exponent, and it also represents the logarithm. Therefore, a logarithm is an exponent.## What is a logarithm in one word?

Definition of logarithm

: **the exponent that indicates the power to which a base number is raised to produce a given number** the logarithm of 100 to the base 10 is 2. Other Words from logarithm More Example Sentences Phrases Containing logarithm Learn More About logarithm.

## What is another name for logarithm?

What is another word for logarithm?

numeric | arithmetic |
---|---|

integrated | logarithmic |

mathematical | numeral |

numerary | numerical |

statistical |

## How will you define logarithmic equation?

A logarithmic equation is

**an equation that involves the logarithm of an expression containing a variable**. To solve exponential equations, first see whether you can write both sides of the equation as powers of the same number.## What are the rules of logarithm?

The rules apply for any logarithm logbx, except that you have to replace any occurence of e with the new base b. The natural log was defined by equations (1) and (2).

…

Basic rules for logarithms.

…

Basic rules for logarithms.

Rule or special case | Formula |
---|---|

Quotient | ln(x/y)=ln(x)−ln(y) |

Log of power | ln(xy)=yln(x) |

Log of e | ln(e)=1 |

Log of one | ln(1)=0 |

## What are the 7 Laws of logarithms?

**Rules of Logarithms**

- Rule 1: Product Rule. The logarithm of the product is the sum of the logarithms of the factors.
- Rule 2: Quotient Rule. …
- Rule 3: Power Rule. …
- Rule 4: Zero Rule. …
- Rule 5: Identity Rule. …
- Rule 6: Inverse Property of Logarithm. …
- Rule 7: Inverse Property of Exponent. …
- Rule 8: Change of Base Formula.

## Who invented the logarithm and why?

**John Napier**, the Scottish mathematician, published his discovery of logarithms in 1614. His purpose was to assist in the multiplication of quantities that were then called sines. The whole sine was the value of the side of a right angled triangle with a large hypotenuse, say 10

^{7}units long.

## What is the difference between logarithmic and exponential?

**Logarithmic functions are the inverses of exponential functions**. The inverse of the exponential function y = a

^{x}is x = a

^{y}. The logarithmic function y = log

_{a}x is defined to be equivalent to the exponential equation x = a

^{y}.

## Is logarithmic the same as exponential?

An exponential function has the form ax, where a is a constant; examples are 2x, 10x, ex.

**The logarithmic functions are the inverses of the exponential functions**, that is, functions that “undo” the exponential functions, just as, for example, the cube root function “undoes” the cube function: 3√23=2.## Where is logarithm used in real life?

Logarithms are used for

**measuring the magnitude of earthquakes**. Logarithms are used for measuring the noise levels in dBs (decibels). They are used to measure the pH level of chemicals. Logarithms are used in radioactivity, mainly to detect the half life of a radioactive element.## What is the opposite of logarithm?

The inverse of a logarithmic function is an

**exponential function**.## What is equation in logarithmic form?

For example, the y = bx is equivalent to

**x = logb**. Both equations have a b, the base, an x, and a y. You can convert from exponential to log form simply by memorizing the pattern. Whatever was in the exponent in the exponential form (in red) goes by itself, on the other side of the equals sign, in the logarithmic form.## What is logarithmic relationship?

**The power to which a base, such as 10, must be raised to produce a given number**. If n

^{x}= a, the logarithm of a, with n as the base, is x; symbolically, log

_{n}a = x. For example, 10

^{3}= 1,000; therefore, log

_{10}1,000 = 3.

## What is a log without base?

When there’s no base on the log, it means that you’re dealing with the

**common logarithm**, which always has a base of 10.## How do you solve logarithms?

To solve a logarithm, start by identifying the base, which is “b” in the equation, the exponent, which is “y,” and the exponential expression, which is “x.” Then, move the exponential expression to one side of the equation, and apply the exponent to the base by multiplying the base by itself the number of times …

## What are the parts of a logarithm called?

**The integer part is called the characteristic of the logarithm, and the fractional part is called the mantissa**.

## What are the 7 Laws of logarithms?

**Rules of Logarithms**

- Rule 1: Product Rule. The logarithm of the product is the sum of the logarithms of the factors.
- Rule 2: Quotient Rule. …
- Rule 3: Power Rule. …
- Rule 4: Zero Rule. …
- Rule 5: Identity Rule. …
- Rule 6: Inverse Property of Logarithm. …
- Rule 7: Inverse Property of Exponent. …
- Rule 8: Change of Base Formula.

## What is log2 value?

The value of log 2, to the base 10, is

**0.301**. The log function or logarithm function is used in most mathematical problems that hold the exponential functions.