Answer:
7) ![4 \ log_3(x) - 4 \ log_3(y)](https://tex.z-dn.net/?f=4%20%5C%20log_3%28x%29%20-%204%20%5C%20log_3%28y%29)
9) ![5log_4(7) - 5log_4(12)](https://tex.z-dn.net/?f=5log_4%287%29%20-%205log_4%2812%29)
11) ![5log_5 \ (x) - log_5 \ (y)](https://tex.z-dn.net/?f=5log_5%20%5C%20%28x%29%20-%20log_5%20%5C%20%28y%29)
Step-by-step explanation:
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Use Logarithm of a Quotient which states
![log_b \frac{M}{N} = log_b M-log_bN](https://tex.z-dn.net/?f=log_b%20%5Cfrac%7BM%7D%7BN%7D%20%20%3D%20log_b%20M-log_bN)
And also use Logarithm of a Power which states
![log_b\ M^{n} = n\log_bM](https://tex.z-dn.net/?f=log_b%5C%20M%5E%7Bn%7D%20%3D%20n%5Clog_bM)
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So using these two properties,
7. ![4 \ log_3(x) - 4 \ log_3(y)](https://tex.z-dn.net/?f=4%20%5C%20log_3%28x%29%20-%204%20%5C%20log_3%28y%29)
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For #9, use the same logarithm propertied
![log_4(\frac{7}{12})^5 = 5log_4(7) - 5log_4(12)](https://tex.z-dn.net/?f=log_4%28%5Cfrac%7B7%7D%7B12%7D%29%5E5%20%3D%205log_4%287%29%20-%205log_4%2812%29)
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#11 is also the same concept
![log_5\ \frac{x^5}{y} = 5log_5 \ (x) - log_5 \ (y)](https://tex.z-dn.net/?f=log_5%5C%20%5Cfrac%7Bx%5E5%7D%7By%7D%20%3D%205log_5%20%5C%20%28x%29%20-%20log_5%20%5C%20%28y%29)
It is not - 5 log5(y) since only x is to the power of 5 not y
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Hope this is what you were looking for and helps you! Have a nice day/night :)