# What is the product of logs?

## 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.

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.