<h2>ANSWER:</h2><h2>49.2 </h2>
Based on your question Two forces of 19.8 pounds and 36.5 pounds act on a body with an angle of 61.4 degrees between them.
After setting up the vectors on the plane and doing the required math
The answer is 49.2 pounds
<h2 />
To simplify we need recall and apply the properties and laws of logarithms.
1)
![log_{2}(32) + ln(e) + log_{10}(100)](https://tex.z-dn.net/?f=%20log_%7B2%7D%2832%29%20%2B%20ln%28e%29%20%2B%20log_%7B10%7D%28100%29%20)
![log_{2}(32) + log_{e}(e) + log_{10}(100)](https://tex.z-dn.net/?f=%20log_%7B2%7D%2832%29%20%2B%20log_%7Be%7D%28e%29%20%2B%20log_%7B10%7D%28100%29)
We need consider the base of each logarithm and express the numbers in the parentheses to each base raised to a certain index. or exponent.
That is
![{2}^{5} = 32 \\ \\ {10}^{2} = 100](https://tex.z-dn.net/?f=%20%7B2%7D%5E%7B5%7D%20%3D%2032%20%5C%5C%20%5C%5C%20%7B10%7D%5E%7B2%7D%20%3D%20100)
As for the middle expression, the base and the number are equal so let us keep it for now.
Our expression now becomes,
![log_{2}( {2}^{5} ) + log_{e}(e) + log_{10}( {10}^{2} )](https://tex.z-dn.net/?f=%20log_%7B2%7D%28%20%7B2%7D%5E%7B5%7D%20%29%20%2B%20log_%7Be%7D%28e%29%20%2B%20log_%7B10%7D%28%20%7B10%7D%5E%7B2%7D%20%29)
Recall this law of logarithm,
![log_{a}( {m}^{n} ) = n log_{a}(m)](https://tex.z-dn.net/?f=%20log_%7Ba%7D%28%20%7Bm%7D%5E%7Bn%7D%20%29%20%3D%20n%20log_%7Ba%7D%28m%29)
![5 log_{2}( {2}) + log_{e}(e) + 2log_{10}( {10} )](https://tex.z-dn.net/?f=5%20log_%7B2%7D%28%20%7B2%7D%29%20%2B%20log_%7Be%7D%28e%29%20%2B%202log_%7B10%7D%28%20%7B10%7D%20%29)
Recall again that,
![log_{a}(a) ,a \ne0 \: or \: 1](https://tex.z-dn.net/?f=%20log_%7Ba%7D%28a%29%20%2Ca%20%5Cne0%20%5C%3A%20or%20%5C%3A%201)
Therefore our expression becomes,
![5 (1) + (1) + 2(1) = 5 + 1 + 2 = 8](https://tex.z-dn.net/?f=5%20%281%29%20%2B%20%281%29%20%2B%202%281%29%20%3D%205%20%2B%201%20%2B%202%20%3D%208)
2) We use change of base to solve this logarithmic equation.
![log_{3}(x) + 4log_{9}(x) = 9](https://tex.z-dn.net/?f=%20log_%7B3%7D%28x%29%20%2B%204log_%7B9%7D%28x%29%20%3D%209)
![log_{3}(x) + log_{9}( {x}^{4} ) = 9](https://tex.z-dn.net/?f=log_%7B3%7D%28x%29%20%2B%20log_%7B9%7D%28%20%7Bx%7D%5E%7B4%7D%20%29%20%3D%209)
It will be easier and faster to change the base to 3.
Recall that,
![\log_{x}(y)=\frac{log_{a}(y)}{log_{a}(x)}](https://tex.z-dn.net/?f=%5Clog_%7Bx%7D%28y%29%3D%5Cfrac%7Blog_%7Ba%7D%28y%29%7D%7Blog_%7Ba%7D%28x%29%7D)
We apply this law to obtain,
![log_{3}(x) + \frac{log_{3}( {x}^{4})}{log_{3}(9) } = 9](https://tex.z-dn.net/?f=log_%7B3%7D%28x%29%20%2B%20%5Cfrac%7Blog_%7B3%7D%28%20%7Bx%7D%5E%7B4%7D%29%7D%7Blog_%7B3%7D%289%29%20%7D%20%3D%209)
![log_{3}(x) + \frac{log_{3}( {x}^{4})}{log_{3}( {3}^{2} ) } = 9](https://tex.z-dn.net/?f=log_%7B3%7D%28x%29%20%2B%20%5Cfrac%7Blog_%7B3%7D%28%20%7Bx%7D%5E%7B4%7D%29%7D%7Blog_%7B3%7D%28%20%7B3%7D%5E%7B2%7D%20%29%20%7D%20%3D%209)
![log_{3}(x) + \frac{log_{3}( {x}^{4})}{2log_{3}( {3} ) } = 9](https://tex.z-dn.net/?f=log_%7B3%7D%28x%29%20%2B%20%5Cfrac%7Blog_%7B3%7D%28%20%7Bx%7D%5E%7B4%7D%29%7D%7B2log_%7B3%7D%28%20%7B3%7D%20%29%20%7D%20%3D%209)
![log_{3}(x) + \frac{log_{3}( {x}^{4})}{2(1) } = 9](https://tex.z-dn.net/?f=log_%7B3%7D%28x%29%20%2B%20%5Cfrac%7Blog_%7B3%7D%28%20%7Bx%7D%5E%7B4%7D%29%7D%7B2%281%29%20%7D%20%3D%209)
![log_{3}(x) + \frac{log_{3}( {x}^{4})}{2} = 9](https://tex.z-dn.net/?f=log_%7B3%7D%28x%29%20%2B%20%5Cfrac%7Blog_%7B3%7D%28%20%7Bx%7D%5E%7B4%7D%29%7D%7B2%7D%20%3D%209)
multiplying through by 2 gives,
![2log_{3}(x) + log_{3}( {x}^{4} ) = 18](https://tex.z-dn.net/?f=2log_%7B3%7D%28x%29%20%2B%20log_%7B3%7D%28%20%7Bx%7D%5E%7B4%7D%20%29%20%3D%2018)
![log_{3}( {x}^{2} ) + log_{3}( {x}^{4} ) = 18](https://tex.z-dn.net/?f=log_%7B3%7D%28%20%7Bx%7D%5E%7B2%7D%20%29%20%2B%20log_%7B3%7D%28%20%7Bx%7D%5E%7B4%7D%20%29%20%3D%2018)
![log_{3}( {x}^{4} \times {x}^{2} ) = 18](https://tex.z-dn.net/?f=%20log_%7B3%7D%28%20%7Bx%7D%5E%7B4%7D%20%5Ctimes%20%7Bx%7D%5E%7B2%7D%20%29%20%3D%2018)
We apply the multiplication law of exponents to obtain,
![log_{3}( {x}^{4 + 2} ) = 18](https://tex.z-dn.net/?f=%20log_%7B3%7D%28%20%7Bx%7D%5E%7B4%20%2B%202%7D%20%29%20%3D%2018)
![log_{3}( {x}^{6} ) = 18](https://tex.z-dn.net/?f=%20log_%7B3%7D%28%20%7Bx%7D%5E%7B6%7D%20%29%20%3D%2018)
We take antilogarithms to get,
![{x}^{6} = {3}^{18}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B6%7D%20%3D%20%7B3%7D%5E%7B18%7D%20)
![{x}^{6} = ( {3}^{3} ) ^{6}](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B6%7D%20%3D%20%28%20%7B3%7D%5E%7B3%7D%20%29%20%5E%7B6%7D%20)
![x = {3}^{3}](https://tex.z-dn.net/?f=x%20%3D%20%7B3%7D%5E%7B3%7D%20)
![x = 27](https://tex.z-dn.net/?f=x%20%3D%2027)
Hence x is 27.
I think 2. 3. 4. :)))))))))
Answer:
88 14/16
Step-by-step explanation:
I call these mixed numbers, a mixed number is written as a b/c and it means
![a+\frac{b}{c}](https://tex.z-dn.net/?f=a%2B%5Cfrac%7Bb%7D%7Bc%7D)
So, we can use the above to re arrange our expression to a more convenient presentation.
we have>
![20+\frac{9}{16} + 24+\frac{5}{8} + 21+\frac{5}{16}+23+\frac{3}{8}\\ \\88+\frac{14}{16} +\frac{8}{8} \\\\89+\frac{14}{16}](https://tex.z-dn.net/?f=20%2B%5Cfrac%7B9%7D%7B16%7D%20%2B%2024%2B%5Cfrac%7B5%7D%7B8%7D%20%2B%2021%2B%5Cfrac%7B5%7D%7B16%7D%2B23%2B%5Cfrac%7B3%7D%7B8%7D%5C%5C%20%20%5C%5C88%2B%5Cfrac%7B14%7D%7B16%7D%20%2B%5Cfrac%7B8%7D%7B8%7D%20%5C%5C%5C%5C89%2B%5Cfrac%7B14%7D%7B16%7D)
88 14/16, we tend to no simplify this expression anymore since, the number 14/16 usually means something in real life, like the diameter for a construction pipe
I believe so ,,,,,,,,,,,,,,,,,,,,