Chapter 8.5, Problem 68HP

To determine

To explain: The relation between the properties of exponent and logarithms and illustrate the Product property but with the Quotient Property and Power property of Logarithms.

Answer to Problem 68HP

The exponents and logarithms are inverse functions of each other and the example to illustrate the Product property but with the Quotient Property and Power property of Logarithms is $3\left({\log }_{5}x+{\log }_{5}y\right)={\log }_5{\left(xy\right)}^3$ .

Explanation of Solution

Given:

The Quotient Property and Power property of Logarithms is given.

Calculation:

The exponents and logarithms are inverse functions of each other, which means their properties are also inverses of each other’s.

The example to illustrate the Product property but with the Quotient Property and Power property of Logarithms is as follows.

  $3\left({\log }_{5}x+{\log }_{5}y\right)={\log }_5{\left(xy\right)}^3$

Therefore, the exponents and logarithms are inverse functions of each other and the example to illustrate the Product property but with the Quotient Property and Power property of Logarithms is $3\left({\log }_{5}x+{\log }_{5}y\right)={\log }_5{\left(xy\right)}^3$ .