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

question 34

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.
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F(x) = log₄ x
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• A)f(x)= log x + log 4 = ln x + ln 4 ?
• B) \[f ( x ) = \frac { \log 4 } { \log x } = \frac { \ln 4 } { \ln x }\]
• C) \[f ( x ) = \log \frac { x } { 4 } = \ln \frac { x } { 4 }\]
• D) \[f ( x ) = \log \frac { 4 } { x } = \ln \frac { 4 } { x }\]
• E) \[f ( x ) = \frac { \log x } { \log 4 } = \frac { \ln x } { \ln 4 }\] ?

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Definitions:

Nominal Interest Rate

The proportionate growth in the amount of money that borrowers need to repay to lenders, excluding adjustments for inflation.

Nominal Interest Rates

The interest rate prior to inflation adjustment, denoting the nominal value of interest payments.

Real Interest Rates

The interest rates adjusted for inflation, more accurately reflecting the true cost of borrowing.

Real Interest Rate

The interest rate, once revised for inflation, to represent the actual borrowing cost or the real savings yield.