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

question 115

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_11.7 x

• A) \(f ( x ) = \frac { \log x } { \log 11.7 } = \frac { \ln x } { \ln 11.7 }\)
• B) \(f ( x ) = \frac { \log 11.7 } { \log x } = \frac { \ln 11.7 } { \ln x }\)
• C)f(x) = log x + log 11.7 = ln x + ln 11.7
• D) \(f ( x ) = \log \frac { 11.7 } { x } = \ln \frac { 11.7 } { x }\)
• E) \(f ( x ) = \log \frac { x } { 11.7 } = \ln \frac { x } { 11.7 }\)

---

Definitions:

1940s

A decade spanning from 1940 to 1949 characterized by significant events including World War II and the beginning of the Cold War, impacting global politics and economies.

Economic Growth

The increase in the production of goods and services in an economy over a period of time, typically measured as the percent change in GDP.

Agricultural

Pertaining to the science, art, and business of cultivating soil, producing crops, and raising livestock; farming.

1865

Signifies the year marked by significant events like the end of the American Civil War and the abolition of slavery in the United States following the 13th Amendment.