## What is the product of logs?

The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. The logarithm of a product is the sum of the logarithms of the factors. The logarithm of the ratio or quotient of two numbers is the difference of the logarithms.

### What is the product rule for logarithms?

We have a similar property for logarithms, called the product rule for logarithms, which says that the logarithm of a product is equal to a sum of logarithms. Because logs are exponents, and we multiply like bases, we can add the exponents.

#### What is the product of log A and log B?

This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. The same base, in this case 10, is used throughout the calculation.

**What is a log in maths?**

log: (in math) An abbreviation for logarithm. logarithm: The power (or exponent) to which one base number must be raised — multiplied by itself — to produce another number. For instance, in the base 10 system, 10 must be multiplied by 10 to produce 100. So the logarithm of 100, in a base 10 system, is 2.

**How do you use product properties?**

To find a power of a product, find the power of each factor and then multiply. In general, (ab)m=am⋅bm. am⋅bm=(ab)m.

## What are the log properties?

Comparison of Exponent law and Logarithm law

Properties/Rules | Exponents | Logarithms |
---|---|---|

Product Rule | xp.xq = xp+q | loga(mn) = logam + logan |

Quotient Rule | xp/xq = xp-q | loga(m/n) = logam – logan |

Power Rule | (xp)q = xpq | logamn = n logam |

### Why do we use logarithms?

Logarithms describe changes in terms of multiplication: in the examples above, each step is 10x bigger. With the natural log, each step is “e” (2.71828…) times more. When dealing with a series of multiplications, logarithms help “count” them, just like addition counts for us when effects are added.

#### What do you mean by log?

(Entry 1 of 6) 1 : a usually bulky piece or length of a cut or fallen tree especially : a length of a tree trunk ready for sawing and over six feet (1.8 meters) long.

**What is the logarithm of a product?**

The logarithm of a product is the sum of the logarithms of the factors. The product rule does not apply when the base of the two logarithms are different.

**What does log mean in math?**

Mathematicians use “log” (instead of “ln”) to mean the natural logarithm. This can lead to confusion: So, be careful when you read “log” that you know what base they mean! All of our examples have used whole number logarithms (like 2 or 3), but logarithms can have decimal values like 2.5, or 6.081, etc. Example: what is log10(26)?

## What is log logarithmic series?

Logarithmic Series. Definition. An expansion for loge (1 + x) as a series of powers of x which is valid only, when |x|<1.

### What are the plots of a logarithm function?

Plots of logarithm functions, with three commonly used bases. The special points logb b = 1 are indicated by dotted lines, and all curves intersect in logb 1 = 0. In mathematics, the logarithm is the inverse function to exponentiation.