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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.
Find all the real solutions to cubic equation x^3 + 4x^2 - 10 =0. Use the cubic equation x^3 + 4x^2 - 10 =0 and perform the following call to the bisection method [0, 1, 30] Use
1. Consider a source with 4 symbols {a,b,c,d}. The probability of the 4 symbols are P(a)=0.4, p(b) = 0.1, p(c)=0.2, p(d)= 0.3. a. Design a Huffman codebook for these symbols.
Find out where the following function is increasing & decreasing. A (t ) = 27t 5 - 45t 4 -130t 3 + 150 Solution As with the first problem first we need to take the
1. Consider the following differential equation with initial conditions: t 2 x'' + 5 t x' + 3 x = 0, x(1) = 3, x'(1) = -13. Assume there is a solution of the form: x (t) = t
Consider the function f: N → N, where N is the set of natural numbers, defined by f(n) = n 2 +n+1. Show that the function f is one-one but not onto. Ans: To prove that f is one
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
41x + 53y = 135, 53x +41y =147 Ans: 41x + 53 y = 135, 53 x + 41 y = 147 Add the two equations : Solve it, to get ... x + y = 3 -------(1) Subtract : Solve it , to
approximate value is the precise or the accurate value which is measured to the actual value.., approximation is how close the measured value is to the actual value , for example
The adjoining figure shows the cross-section of a railway tunnel. The radius of the tunnel is 3.5m (i.e., OA=3.5m) and ∠AOB=90 o . Calculate : i. the height of the
seven more than a number is less than or equal to -18
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