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$\frac{20b}{{\left(4b^3\right)}^3}$

1. A body falls from rest against resistance proportional to the square root of the speed at any instant. If the body attains speed V1 and V2 feet per second, after 1 and 2 seconds in motion, respectively, find an expression for the limiting velocity.

Question 71

22+64

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Determine whether the sequence 80,40,20,10,5,... is arithmetic and if it is, what is the common difference

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How do I evaluate the sum $\sum _{n=1,3,5,...}^{\mathrm{\infty }}\frac{1}{n^4}$

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How do you find the length of a curve defined parametrically?

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Probability of geometric mean being higher than 1/6
If we choose 2 numbers from [0,2], independent from each other,what is the probability of their geometric mean being higher than 1/6?

Calculate $$\sqrt{3}(5-3\sqrt{5})$$

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Simplyfing Log Question
Don't know the concepts of diving and multiplying whole logs.
$\frac{{\log }_a\left(x\right)}{{\log }_a\left(y\right)}\cdot \frac{{\log }_b\left(y\right)}{{\log }_b\left(x\right)}$
Can you please tell me how to simplify this?

Given $f(x)=3x^2-4x-1$ and $g(x)=8-2x$, find each of the following:
a) f(2)
b) f(-2)
c) g(1/4)

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Prove equality $a^{{\log }_{b}c}=c^{{\log }_{b}a}$
I'm try to prove the equality:
$a^{{\log }_{b}c}=c^{{\log }_{b}a}$
I'm having trouble finding information regarding this, also I need to figure out why $n^{{\log }_{2}3}$ is better than $3^{{\log }_{2}n}$ as a closed form formula for $M(n)$? Thank you!