Use the Change-Of-Base Formula to Rewrite the Logarithm as a Ratio

question 134

Multiple Choice

Use the change-of-base formula to rewrite the logarithm as a ratio of logarithms.Then use a graphing utility to graph the ratio.
$f ( x ) = \log _ { \frac { 1 } { 5 } } x$

• A) \(f ( x ) = \frac { \log \frac { 1 } { 5 } } { \log x } = \frac { \ln \frac { 1 } { 5 } } { \ln x }\)
• B) \(f ( x ) = \frac { \log x } { \log \frac { 1 } { 5 } } = \frac { \ln x } { \ln \frac { 1 } { 5 } }\)
• C) \(f ( x ) = \log x + \log \frac { 1 } { 5 } = \ln x + \ln \frac { 1 } { 5 }\)
• D) \(f ( x ) = \log \frac { \frac { 1 } { 5 } } { x } = \ln \frac { \frac { 1 } { 5 } } { x }\)
• E) \(f ( x ) = \log \frac { x } { \frac { 1 } { 5 } } = \ln \frac { x } { \frac { 1 } { 5 } }\)

---

Definitions:

Highest Case Price

The maximum price at which a case of goods, typically in a wholesale or retail setting, is offered for sale.

Ontario Ministry

A branch of the government in the province of Ontario, Canada, responsible for a specific department or area of public policy.

Teaching Experience

The duration and quality of time that an individual has spent in the educational field as a teacher.

Stem-And-Leaf Display

A method of displaying quantative data to show its distribution, where each data point is split into a "stem" (the initial digit or digits) and a "leaf" (the last digit).