# What are the 4 properties of logarithm?

## What are the 4 properties of logarithm?

The Four Basic Properties of Logs

- logb(xy) = logbx + logby.
- logb(x/y) = logbx – logby.
- logb(xn) = n logbx.
- logbx = logax / logab.

## What are the 5 properties of logarithms?

In the case of logarithmic functions, there are basically five properties….Reciprocal rule

- Logarithms.
- Logarithmic Functions.
- Logarithm Table.
- Logarithmic Differentiation.

**What is characteristic of a number in logarithm?**

Printable version. The characteristic of a common logarithm (that is, a base 10 logarithm) is its integer part, which indicates the order of magnitude but not the digits of the number. For example, the characteristic of log1020≈1.3010 is 1 while the characteristic of log10600≈2.7782 is 2.

### What are the three main properties of logarithmic functions?

Properties of Logarithms

- Rewrite a logarithmic expression using the power rule, product rule, or quotient rule.
- Expand logarithmic expressions using a combination of logarithm rules.
- Condense logarithmic expressions using logarithm rules.

### What are the 7 Laws of logarithms?

Rules of Logarithms

- Rule 1: Product Rule.
- Rule 2: Quotient Rule.
- Rule 3: Power Rule.
- Rule 4: Zero Rule.
- Rule 5: Identity Rule.
- Rule 6: Log of Exponent Rule (Logarithm of a Base to a Power Rule)
- Rule 7: Exponent of Log Rule (A Base to a Logarithmic Power Rule)

**What are the conditions of log?**

The logarithmic function y = logax is defined to be equivalent to the exponential equation x = ay. y = logax only under the following conditions: x = ay, a > 0, and a≠1. It is called the logarithmic function with base a. Consider what the inverse of the exponential function means: x = ay.

#### What is the difference between characteristics and mantissa?

As nouns the difference between mantissa and characteristic is that mantissa is (obsolete) a minor addition to a text while characteristic is a distinguishable feature of a person or thing.

#### What are the characteristic properties of the graphs of logarithmic functions?

A General Note: Characteristics of the Graph of the Parent Function f(x)=logb(x)

- one-to-one function.
- vertical asymptote: x = 0.
- domain: (0,∞) ( 0 , ∞ )
- range: (−∞,∞) ( − ∞ , ∞ )
- x-intercept: (1,0) and key point (b,1) ( b , 1 )
- y-intercept: none.
- increasing if b>1. b > 1.
- decreasing if 0 < b < 1.