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Answer:
![x=32768.000](https://tex.z-dn.net/?f=x%3D32768.000)
Step-by-step explanation:
One is given the following expression:
![log_2(x)+log_4(x)=5](https://tex.z-dn.net/?f=log_2%28x%29%2Blog_4%28x%29%3D5)
Use the logarithm base change rule, which states the following:
![log_b(y)=\frac{log(y)}{log(b)}](https://tex.z-dn.net/?f=log_b%28y%29%3D%5Cfrac%7Blog%28y%29%7D%7Blog%28b%29%7D)
Remember, a logarithm with not base indicated is another way of writing a logarithm to the base of (10). One can apply the base change rule to this situation:
![log_2(x)+log_4(x)=5](https://tex.z-dn.net/?f=log_2%28x%29%2Blog_4%28x%29%3D5)
![\frac{log(x)}{log(2)}+\frac{log(x)}{log(4)}=5](https://tex.z-dn.net/?f=%5Cfrac%7Blog%28x%29%7D%7Blog%282%29%7D%2B%5Cfrac%7Blog%28x%29%7D%7Blog%284%29%7D%3D5)
Factor out (log(x)),
![(log(x))(\frac{1}{log(2)}+\frac{1}{log(4)})=5](https://tex.z-dn.net/?f=%28log%28x%29%29%28%5Cfrac%7B1%7D%7Blog%282%29%7D%2B%5Cfrac%7B1%7D%7Blog%284%29%7D%29%3D5)
Inverse operations:
![log(x)=\frac{5}{\frac{1}{(log(2)+log(4)}}](https://tex.z-dn.net/?f=log%28x%29%3D%5Cfrac%7B5%7D%7B%5Cfrac%7B1%7D%7B%28log%282%29%2Blog%284%29%7D%7D)
Simplify,
![log(x)=5(log(2)+log(4))](https://tex.z-dn.net/?f=log%28x%29%3D5%28log%282%29%2Blog%284%29%29)
![log(x)=4.51545](https://tex.z-dn.net/?f=log%28x%29%3D4.51545)
Now rewrite the logarithm, remember, a logarithm is another way of writing an exponent, in the following format:
![b^x=y\ \ -> log_b(y)=x](https://tex.z-dn.net/?f=b%5Ex%3Dy%5C%20%5C%20-%3E%20log_b%28y%29%3Dx)
![log(x)=4.51545](https://tex.z-dn.net/?f=log%28x%29%3D4.51545)
![10^4^.^5^1^5^4^5=x](https://tex.z-dn.net/?f=10%5E4%5E.%5E5%5E1%5E5%5E4%5E5%3Dx)
![32768.000=x](https://tex.z-dn.net/?f=32768.000%3Dx)
Answer:
Step-by-step explanation:
<u>Average rate of change between x = 2 and x = 4 is:</u>
- [f(4) - f(2)]/(4 - 2) =
- (3*4³ - 1 - 3*2³ + 1)/2 =
- 168/2 =
- 84
<span>y= 7/2 = 1/2 (x-4)
its written in the question</span>