Chapter 8.4, Problem 43HP

(a)

To determine

To Find: The appropriate term and explain the reasoning for the given condition for the logarithm equations of the form $y={\log }_{b}x$ .

Answer to Problem 43HP

The value is less than 0.

Explanation of Solution

Given:

If the base of logarithmic equation is greater than 1 and value of $x$ is between 0 and 1 then the value of y is (less than, greater than, equal to 0)

Calculation:

Consider that if the base of the logarithm equation is more than 1 and the value of the $x$ is between 0 and 1 then the value is less than 0.

(b)

To determine

To Find: The appropriate term and explain the reasoning for the given condition for the logarithm equations of the form $y={\log }_{b}x$ .

Answer to Problem 43HP

The value of y is less than 0.

Explanation of Solution

Given:

If the base of logarithmic equation is between 0 and1 and the value of x is more than 1 and then the value of y is (less than, greater than, equal to) 0.

Calculation:

Consider that the base of the logarithm is between 0 and 1 and the value of x is more than 1 and the value of y is less than 0.

(c)

To determine

To Find: The appropriate term and explain the reasoning for the given condition for the logarithm equations of the form $y={\log }_{b}x$ .

Answer to Problem 43HP

There is no solution for the function $y={\log }_{b}0$ .

Explanation of Solution

Given:

There is/are (no, one, infinitely many) solutions for $b$ in the equation $y={\log }_{b}0$ .

Calculation:

Consider the given function is $y={\log }_0\left(1\right)$ .

The above equation has many solution for $b$ as 1 logarithm is 0.

(d)

To determine

To Find: The appropriate term and explain the reasoning for the given condition for the logarithm equations of the form $y={\log }_{b}x$ .

Answer to Problem 43HP

The function has infinitely many solution.

Explanation of Solution

Given:

There is/are (no, one, infinitely many) solutions for $b$ in the equation $y={\log }_{b}1$ .

Calculation:

Consider the given function is $y={\log }_{b}1$ .

The above equation has many solution for $b$ as 1 logarithm is 0 so the function has infinitely many solution.