## What are the properties of logarithmic inequalities?

Logarithmic inequalities are inequalities in which one (or both) sides involve a logarithm. Like exponential inequalities, they are useful in analyzing situations involving repeated multiplication, such as in the cases of interest and exponential decay.

### What is the reversal property of inequality?

Property 3 – Multiplying by a Negative Number The sense of the inequality is reversed if both sides are multiplied or divided by the same negative number.

**What is comparison property of inequality?**

Comparison property: If x = y + z and z > 0 then x > y. Example: 6 = 4 + 2, then 6 > 4. The properties of inequality are more complicated to understand than the property of equality.

**What is the addition property of inequality?**

The addition property for inequalities states that if an inequality exists, adding or subtracting the same number on both sides does not change the inequality.

## What is the trichotomy property?

noun Mathematics. the property that for natural numbers a and b, either a is less than b, a equals b, or a is greater than b. Also called law of trichotomy, trichotomy law, trichotomy principle.

### 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 is the property of equality for logarithmic equations?**

The equality rule says that if you have two logarithms with the same base that are equivalent, then what is inside the logarithms are equivalent to each other.

**What are the basic properties of logarithms?**

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 steps in solving a logarithmic equation inequality?

Solving Logarithmic Equations

- Step 1: Use the rules of exponents to isolate a logarithmic expression (with the same base) on both sides of the equation.
- Step 2: Set the arguments equal to each other.
- Step 3: Solve the resulting equation.
- Step 4: Check your answers.
- Solve.

### What are the properties of trichotomy in math?

Math Properties – Trichotomy -. Properties of Inequality : In mathematics, inequalities compare numbers and expressions that are not equal to one another. Generally, the following symbols are used for comparison: , , , . Each of these symbols compares the relative size of two numbers to show which number is bigger, and which number is smaller.

**How do you work out logarithmic inequalities?**

Introduction. The key to working with logarithmic inequalities is the following fact: If a > 1 and x > y, then logax > logay. Otherwise, if 0 < a < 1, then logax < logay. Of course, the base of a logarithm cannot be 1 or nonpositive. More importantly, the converse is true as well: If a > 1 and logax > logay, then x > y.

**What is the definition of logarithmic function?**

Logarithmic Function Definition. In mathematics, the logarithmic function is an inverse function to exponentiation. The logarithmic function is defined as. For x > 0 , a > 0, and a 1, y= log a x if and only if x = a y. Then the function is given by.