QUESTION 1
The given logarithm is
We apply the power rule of logarithms; 
We now apply the product rule of logarithm;
QUESTION 2
The given logarithm is
We apply the power rule of logarithm to get;
We apply the product to obtain;
We apply the quotient rule; 
![=\log_5(\frac{x^8 \sqrt[4]{y^3} }{z^5})](https://tex.z-dn.net/?f=%3D%5Clog_5%28%5Cfrac%7Bx%5E8%20%5Csqrt%5B4%5D%7By%5E3%7D%20%7D%7Bz%5E5%7D%29)
Answer:
6
Step-by-step explanation:
The 4 and 12 are multiplied together which creates 48 (4*12). Then you divide the 48 by 8 (48/8) wich equals 6.
You have 3 unknowns: a, b, and c. That means you have to have 3 equations to solve for the values of them. 3 unknowns needs 3 different equations. We will use the first 3 points in the table and thank God that one of them has an x value of 0. We will replace the x and y in the general form of the quadratic with the x and y from the table, 3 times, to find each variable. Watch how it works. We will start with (0, 15).
. That gives us right away that c = 15. We will do the same thing again with the second value in the table along with the fact that c = 15 to get an equation in a and b.
which simplifies to
4a+2b=.5. Now do the same for the third set of coordinates from the table.
which simplifies down to
16a+4b=2. Solve those simultaneously. Multiply the first bolded equation by -4 and then add that one to the second bolded one.
gives us
-16a-8b=-2. Add that to the second bolded equation and the a terms cancel out giving us -4b=0 so b = 0. Subbing that back in we solve for a: 16a+4(0)=2 and 16a = 2. Therefore, a = 1/8. The quadratic then is
The roots of 54 are: 1 and 54, 2 and 27, 3 and 18, 6 and 9, then it restarts all over again.
The two numbers have to multiply up to 54, and add up to 3. 9 and 6 have a difference of 3, and the multiplied sum is negative, so this is your pair.
9 and -6 fit this criteria, since they add up to 3 and multiply to 64.
