Chapter 12.3, Problem 1PE

(a)

To determine

To fill: The blank spaces given in the statement, ‘the function defined by $y={\log }_{b}x$ is called the ___ function with base __. The values of x and b are positive, and $b\ne 1$ .’

(b)

To determine

To fill: The blank spaces given in the statement, ‘given $y={\log }_{b}x$, we call y the ___, we call b the ___, and we call x the ___.

(c)

To determine

To fill: The blank spaces given in the statement, ‘in interval notation, the domain of $y={\log }_{b}x$ is ___ and the range is ___.’

(d)

To determine

To fill: The blank space given in the statement, ‘a logarithmic function base b is the inverse of the ___ function base b’.

(e)

To determine

To fill: The blank space given in the statement, ‘the logarithmic function base 10 is called the ___ logarithmic function and is denoted by $y=\log x$ ’.

(f)

To determine

Whether the graph of a logarithmic function is increasing/decreasing if the base $b>1$, whereas the graph is increasing/decreasing if the base is between 0 and 1.

(g)

To determine

Which values out of $x=2,x=3,x=4,x=5\text{ and }x=6$, are not in the domain of $y=\log \left(x-4\right)$.

(h)

To determine

To fill: The blank space given in the statement, ‘the graph of a logarithmic function base b and an exponential function base b are symmetric with respect to the line ___’.