Use Properties of Logarithms to Expand the Logarithmic Expression as Much

question 61

Multiple Choice

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate
logarithmic expressions without using a calculator.
- $$\log \left[ \frac { 8 x ^ { 4 } \sqrt [ 4 ] { 5 - x } } { 3 ( x + 5 ) ^ { 2 } } \right]$$

• A) \(\log 8 + 4 \log x + \frac { 1 } { 4 } \log ( 5 - x ) - \log 3 - 2 \log ( x + 5 )\)
• B) \(\log 8 + \log x ^ { 4 } + \log ( 5 - x ) ^ { 1 / 4 } - \log 3 - \log ( x + 5 ) ^ { 2 }\)
• C) \(\log \left( 8 x ^ { 4 } \sqrt [ 4 ] { 5 - x } \right) - \log \left( 3 ( x + 5 ) ^ { 2 } \right)\)
• D) \(\log 8 + 4 \log x + \frac { 1 } { 4 } \log ( 5 - x ) - \log 3 + 2 \log ( x + 5 )\)