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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.
Find the middle term of the AP 1, 8, 15....505. A ns: Middle terms a + (n-1)d = 505 a + (n-1)7 = 505 n - 1 = 504/7 n = 73 ∴ 37th term is middle term a 37
Lori ran (5)1/2 miles Monday, (6)1/4 miles Tuesday (4)1/2 miles Wednesday and (2)3/4 mile on Thursday what is the average number of miles lori ran ? To find the average, add
1. In an in finite horizon capital/consumption model, if kt and ct are the capital stock and consumption at time t, we have f(kt) = ct+kt+1 for t ≥ 0 where f is a given production
we know that derivative of x 2 =2x. now we can write x 2 as x+x+x....(x times) then if we take defferentiation we get 1+1+1+.....(x times) now adding we get x . then which is wro
52/7
area and perimetre of semi circle
Multistage sampling Multistage sampling is similar to stratified sampling except division is done on geographical/location basis, for illustration a country can be divided into
Go back to the complex numbers code in Figures 50 and 51 of your notes. Add code fragments to handle the following: 1. A function for adding two complex numbers given in algeb
Calculate the Probability A bag contains 80 balls of such 20 are red, 25 are blue and 35 are white. A ball is picked at random what is the probability that the ball picked is
Level Curves or Contour Curves Another topic that we should look at is that of level curves or also known as contour curves. The level curves of the function z = f (x, y) are t
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