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

  1. Step 1: Use the rules of exponents to isolate a logarithmic expression (with the same base) on both sides of the equation.
  2. Step 2: Set the arguments equal to each other.
  3. Step 3: Solve the resulting equation.
  4. Step 4: Check your answers.
  5. 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.

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