Part 1: Is the following equation true (2 points)
Part 2: Part 2: Use complete sentences to explain the properties in making your decision. (6 points)
$$4 \log _{3} x + \frac{ 1 }{ 2 } \log _{3} y - 2 \log _{3} z =\log \frac{ x ^{4}\sqrt{y} }{ z ^{2} }$$

Question

Part 1: Is the following equation true (2 points)
Part 2: Part 2: Use complete sentences to explain the properties in making your decision. (6 points)
$$4 \log  _{3} x + \frac{ 1 }{ 2 } \log _{3} y - 2 \log _{3} z =\log \frac{ x ^{4}\sqrt{y} }{ z ^{2} }$$

campbell_st · Answer

well this uses 3 different log laws

1. powers 
$$a \log(b) =  \log(b^a)$$

2. addition & multiplication

$$\log(a) + \log(b) = \log(ab)$$

3. subtraction/division

$$\log(a) - \log(b) = \log(\frac{a}{b})$$

you need to use all 3 

start by using the power law for all 3 logs...