Option B:
is the correct answer.
Explanation:
The exponential equation is ![e^{5 x}=6](https://tex.z-dn.net/?f=e%5E%7B5%20x%7D%3D6)
If
, then ![\ln (f(x))=\ln (g(x))](https://tex.z-dn.net/?f=%5Cln%20%28f%28x%29%29%3D%5Cln%20%28g%28x%29%29)
Thus, the equation becomes
![\ln \left(e^{5 x}\right)=\ln (6)](https://tex.z-dn.net/?f=%5Cln%20%5Cleft%28e%5E%7B5%20x%7D%5Cright%29%3D%5Cln%20%286%29)
Applying log rule,
and thus the equation becomes
![5 x \ln (e)=\ln (6)](https://tex.z-dn.net/?f=5%20x%20%5Cln%20%28e%29%3D%5Cln%20%286%29)
Since, we know that,
, using this we get,
![5 x=\ln (6)](https://tex.z-dn.net/?f=5%20x%3D%5Cln%20%286%29)
Hence, the logarithmic equation which is equivalent to the exponential equation
is ![\ln 6=5 x](https://tex.z-dn.net/?f=%5Cln%206%3D5%20x)
Thus, Option B is the correct answer.
Answer:
The value of x that gives the maximum transmission is 1/√e ≅0.607
Step-by-step explanation:
Lets call f the rate function f. Note that f(x) = k * x^2ln(1/x), where k is a positive constant (this is because f is proportional to the other expression). In order to compute the maximum of f in (0,1), we derivate f, using the product rule.
![f'(x) = k*((x^2)'*ln(1/x) + x^2*(ln(1/x)')) = k*(2x\,ln(1/x)+x^2*(\frac{1}{1/x}*(-\frac{1}{x^2})))\\= k * (2x \, ln(1/x)-x)](https://tex.z-dn.net/?f=f%27%28x%29%20%3D%20k%2A%28%28x%5E2%29%27%2Aln%281%2Fx%29%20%2B%20x%5E2%2A%28ln%281%2Fx%29%27%29%29%20%3D%20k%2A%282x%5C%2Cln%281%2Fx%29%2Bx%5E2%2A%28%5Cfrac%7B1%7D%7B1%2Fx%7D%2A%28-%5Cfrac%7B1%7D%7Bx%5E2%7D%29%29%29%5C%5C%3D%20k%20%2A%20%282x%20%5C%2C%20ln%281%2Fx%29-x%29)
We need to equalize f' to 0
- k*(2x ln(1/x) - x) = 0 -------- We send k dividing to the other side
- 2x ln(1/x) - x = 0 -------- Now we take the x and move it to the other side
- 2x ln(1/x) = x -- Now, we send 2x dividing (note that x>0, so we can divide)
- ln(1/x) = x/2x = 1/2 ------- we send the natural logarithm as exp
- 1/x = e^(1/2)
- x = 1/e^(1/2) = 1/√e ≅ 0.607
Thus, the value of x that gives the maximum transmission is 1/√e.
Answer:
3
Step-by-step explanation:
Answer:omg I gotchu I just learned these for the letters for example would be q/1 times 2/7 because if you have one letter or number you ALWAYS put a one under it then u multiply another easy trick don’t butterfly multiply go straight across and example 8/1 (all ways add the one) times 3/4. Ok how to multiply that always go across so it would be 8x3 and 1x4 your answer should be 24/4 and simplify if needed
Step-by-step explanation:
Your answer would be ten times the ingredients it would take to make ONE pancake.
What kind of question is this?