Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 134

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- $\log _ { 7 } \left( \frac { \sqrt [ 5 ] { m } \sqrt [ 6 ] { n } } { k ^ { 2 } } \right)$

• A) \(\frac { 1 } { 5 } \log _ { 7 } \mathrm {~m} + \frac { 1 } { 6 } \log _ { 7 } \mathrm { n } - 2 \log _ { 7 } \mathrm { k }\)
• B) \(\frac { 1 } { 5 } \log _ { 7 } \mathrm {~m} \cdot \frac { 1 } { 6 } \log _ { 7 } \mathrm { n } \div 2 \log _ { 7 } \mathrm { k }\)
• C) \(\frac { 5 } { 7 } \log _ { 7 } \mathrm {~m} + \frac { 6 } { 7 } \log _ { 7 } \mathrm { n } - \frac { 2 } { 7 } \log _ { 7 } \mathrm { k }\)
• D) \(5 \log _ { 7 } \mathrm {~m} + 6 \log _ { 7 } \mathrm { n } - 2 \log _ { 7 } \mathrm { k }\)

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Definitions:

Population

The total number of individuals within a specific group or area being studied or observed.

Strip Bond

A bond that has had its coupon payments and principal repayment detached and sold separately as zero-coupon bonds.

Compounded Semiannually

A calculation method where interest is applied to the principal plus previously accumulated interest twice per year.

Face Value

The nominal or dollar value printed on a financial instrument such as a bond or stock certificate, representing the value the issuer promises to pay at maturity.