Solving Equations with Logarithms

1)
To get the best performance we first need to take the log of the given equation,
P=0.1298 a2+ b
√4.123 cd
log P=2 log a+ log 0.1298+ 1
b ¿
Now this can be solved using partial differentiation and equating each of the four equations we
obtain,
∂ log P
∂ a =0
∂ log P
∂b =0
∂ log P
∂ c =0
∂ log P
∂ d =0
2)
We can use the concept of projectile motion to solve it. Since the trajectory is a projectile and the
initial velocity and the angle of projection are given, we can use the normal equations of projectile
motion to solve the problem
The velocity will be broken down in to two components one horizontal and the other vertical. The
horizontal component is 25cos16 and the vertical is 25sin16. Then we should find out the time for
which
y=25sin 16 ° t−1
2 g t2
Is satisfied and from the t which we will find out
x=25 cos 16 ° t
3)
The techniques of equation of continuity should be used to solve the problem. A continuity equation
in physics is an equation that describes the transport of some quantity. So the amount of water
flowing per min in to the cylinder if is greater than the amount of water per flowing out per min is
through the hole at the bottom of the cylinder then it will over flow otherwise if it less then it will
become empty
4)