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The logarithm of a provided number b to the base 'a' is the exponent showing the power to which the base 'a' have to be raised to get the number b. This number is defined as log a b. Therefore log a b = x ↔ ax = b, a > 0, a ≠1 and b>0. From the basic definition of the logarithm of the number b to the base 'a', we have an identity
That is called as Fundamental Logarithmic Identity.
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A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of 40% acid solution.
We will firstly notice the undamped case. The differential equation under this case is, mu'' + ku = F(t) It is just a non-homogeneous differential equation and we identify h
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∫1/sin2x dx = ∫cosec2x dx = 1/2 log[cosec2x - cot2x] + c = 1/2 log[tan x] + c Detailed derivation of ∫cosec x dx = ∫cosec x(cosec x - cot x)/(cosec x - cot x) dx = ∫(cosec 2 x
to difine trigonometric ratios of an angle,is it necessary that the initial ray of the angle must be positive x-axis?
The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to
a conical vessel of radius 6cm and height 8cm is completely filled with water.a sphere is lowered into the water and its size is such that when it touches the size it is immersed.w
IF YOU HAVE 24 BISCUITS HOW MUCH WHOLE BISCUITS DO YOU HAVE IF YOU SHARE FIVE BETWEEN 5 FRIENDS
1. Solve the given differential equation, subject to the initial conditions: . x2y''-3xy'+4y = 0 . y(1) = 5, y'(1) = 3 2. Find two linearly independent power series soluti
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