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If x = by where both b > 0, x > 0, then we define y = logb x, which is read as
"y is the log to the base b of x". This means that, logb x or y is the number to which b has to be raised exponentially in order to equal x. So a log is simply the inverse function of an exponential function. Therefore, the domain of any logarithmic function is the set of positive numbers since the range of any exponential function is the set of positive numbers.
Example 20
Let us find the log of 100 to the base 10
As 100 = 102
log10 100 = 2
Similarly,
The exponential function and logarithmic function are inverse functions of each other, since
y = logb x if and only if x = by.
If y = log10 x = f(x), then x = 10y and vice-versa.
If x = ey then y = ln x and vice versa.
The shape of the logarithmic function y = ln x is graphically illustrated below.
How do we add integers
Arc length Formula L = ∫ ds Where ds √ (1+ (dy/dx) 2 ) dx if y = f(x), a x b ds √ (1+ (dx/dy) 2 ) dy
Illustration of Rank Correlation Coefficient Sometimes numerical data such refers to the quantifiable variables may be described after which a rank correlation coefficient may
A certain flight arrives on time 78% of the time. Suppose 1000 flights are randomly selected. Use the normal approximation to the binomial to approximate the probability that
Q. a(b - c)x^2 + b(c - a)x + c(a - b) = 0 has equal roots then b = ? Ans: Condition that a quadratic equation ax² + bx + c = 0 has equal roots is: Its discriminant, b² - 4ac = 0 A
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1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is dierent
tan 2x = 1
Consider a circular disc of radius 1 and thickness 1 which has a uniform density 10 ?(x, y, z) = 1. (a) Find the moment of inertia of this disc about its central axis (that is, the
Tangent Lines : The first problem which we're going to study is the tangent line problem. Before getting into this problem probably it would be best to define a tangent line.
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