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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.
A jar contains 54 marbles each of which is blue , green or white. The probability of selecting a blue marble at random from the jar is 1/3 and the probability of selecting a green
Correlation and Regression Correlation CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of
A tower and a monument stand on a level plane. the angles of depression on top and bottom of the monument viewed from the top of the tower are 13 degrees and 31 degrees, respective
Permutation - It is an order arrangement of items whether the order must be strictly observed Illustration Assume x, y and z be any of three items. Arrange these in all
A cable is attached to a pole 24 ft above ground and fastened to a stake 10 ft from the base of the pole. In sequence to remain the pole perpendicular to the ground, how long is th
Solve following 4e 1+3 x - 9e 5-2 x = 0 . Solution Here the first step is to get one exponential on every side & then we'll divide both sides by one of them (that doesn'
How many 4 digit number lass than 6000 can be made with the digits 7,6,4 and 2 if digits are not repeated?
Squeeze Theorem (Sandwich Theorem and the Pinching Theorem) Assume that for all x on [a, b] (except possibly at x = c ) we have, f ( x )≤ h (
Let G be a group acting on a set X. The action is called faithful if for any g ≠ 1 ∈ G there exists an x ∈ X such that gx ≠ x. That is, only the identity fi xes everything. Prov
Limits The concept of a limit is fundamental in calculus. Often, we are interested to know the behavior of f(x) as the independent variable x approaches some
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