Use the Properties of Logarithms to Expand the Expression $\log _ { 4 } \left[ x ^ { 5 } ( x + 6 ) ^ { 2 } \right]$

question 148

Multiple Choice

Use the properties of logarithms to expand the expression $\log _ { 4 } \left[ x ^ { 5 } ( x + 6 ) ^ { 2 } \right]$ . (Assume $x > 0$ ) .

• A) \(5 \log _ { 4 } x + 2 \log _ { 4 } ( x + 6 )\)
• B) \(5 \log _ { 4 } x \times 2 \log _ { 4 } ( x + 6 )\)
• C) \(\frac { \log _ { 4 } x ^ { 5 } } { \log _ { 4 } ( x + 6 ) ^ { 2 } }\)
• D) \(5 \log _ { 4 } x + \log _ { 4 } ( x + 6 )\)
• E) \(\left( 5 \log _ { 4 } x \right) \times \left( 2 \log _ { 4 } x \right) + 2 \log _ { 4 } 6 x\)

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Definitions:

Short-term Rate

Interest rates on loans or financial products that are due within a short period, usually one year or less, significant for monetary policy and investment decisions.

Reserve Requirements

Regulations set by central banks regarding the minimum amount of reserves that banks must hold against deposits.

Monetary Policy

The process by which a central bank controls the supply of money in an economy, typically to achieve objectives like controlling inflation or promoting growth.

Negative Excess Reserves

A situation where banks have less reserves than the required minimum, potentially leading to liquidity problems.