# Characteristics of logarithmic functions

## What are the 4 properties of logarithm?

The Four Basic Properties of Logs

**log _{b}(xy) = log_{b}x + log_{b}y**. log

_{b}(x/y) = log

_{b}x – log

_{b}y. log

_{b}(x

^{n}) = n log

_{b}x. log

_{b}x = log

_{a}x / log

_{a}b.

## What are three important things to remember about logarithmic functions?

As you’ve seen, there are three essential quantities in a logarithmic equation y = log

_{b}x:**the base b, the exponent y, and the input x**.## What are the properties of a logarithmic graph?

Properties of Graph

**All logarithmic graphs pass through the point**. The domain is: All positive real numbers (not zero). The range is: all real numbers.

## What are the 5 rules 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 are the rules of logarithms?

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)âˆ’ln(y) |

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

Log of e | ln(e)=1 |

Log of one | ln(1)=0 |

## What is the main function of logarithm?

In mathematics, the logarithm is the

**inverse function to exponentiation**. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.## How do you know if a function is logarithmic?

As you can tell from the graph to the right, the logarithmic curve is a reflection of the exponential curve.

…

Comparison of Exponential and Logarithmic Functions.

…

Comparison of Exponential and Logarithmic Functions.

Exponential | Logarithmic | |
---|---|---|

Function | y=a^{x}, a>0, aâ‰ 1 | y=log_{a} x, a>0, aâ‰ 1 |

Domain | all reals | x > 0 |

Range | y > 0 | all reals |

## What kind of function is a logarithmic function?

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}. y = log_{a}x only under the following conditions: x = a^{y}, a > 0, and aâ‰ 1.## How many types of logarithms are there?

**Two kinds of logarithms**are often used in chemistry: common (or Briggian) logarithms and natural (or Napierian) logarithms. The power to which a base of 10 must be raised to obtain a number is called the common logarithm (log) of the number. The power to which the base e (e = 2.718281828…….)

## How do you solve logarithmic properties?

## What are the inverse properties of logarithms?

The inverse properties of the logarithm are

**logb bx=x and blogb x=x where x>0**. The product property of the logarithm allows us to write a product as a sum: logb (xy)=logb x+logb y. The quotient property of the logarithm allows us to write a quotient as a difference: logb (xy)=logb xâˆ’logb y.## What are the properties of e?

Like the constant Ï€, e is

**irrational (it cannot be represented as a ratio of integers) and transcendental (it is not a root of any non-zero polynomial with rational coefficients)**. To 50 decimal places the value of e is: 2.71828182845904523536028747135266249 (sequence A001113 in the OEIS).## What is logarithmic function example?

The logarithm of a number is the exponent to which a fixed value, called the base must be raised to produce that number. For example,

**the log of 1000 to base 10 is 3**, because 1000 is 10 to the third power. In general, the logarithmic function is the inverse of the exponential function.## How do you simplify logarithmic functions?

## What are the examples of logarithmic equation?

LOGARITHMIC EQUATIONS | ||
---|---|---|

Examples | EXAMPLES OF LOGARITHMIC EQUATIONS | |

Log_{2} x = -5 | 5 + ln 2x = 4 | |

ln x + ln (x – 2) = 1 | log_{6} x + log_{6} (x + 1) = 1 | |

Solving | STEPS TO SOLVE A logarithmic EQUATIONS |

## What is the main function of logarithm?

In mathematics, the logarithm is the

**inverse function to exponentiation**. That means the logarithm of a given number x is the exponent to which another fixed number, the base b, must be raised, to produce that number x.## Why are logarithmic functions important?

Logarithmic functions are important largely

**because of their relationship to exponential functions**. Logarithms can be used to solve exponential equations and to explore the properties of exponential functions.## Is logarithmic function continuous?

Examples of

**continuous functions**are power functions, exponential functions and logarithmic functions.## What are the 3 types of logarithms?

The most common types of logarithms are

**common logarithms, where the base is 10, binary logarithms, where the base is 2, and natural logarithms**, where the base is e â‰ˆ 2.71828.## What is the range of logarithmic functions?

The range of a logarithmic function takes all values, which include the positive and negative real number values. Thus the range of the logarithmic function is

**from negative infinity to positive infinity**.