If x = b^y where both b > 0, x > 0, then we define y = log_b x, which is read as

"y is the log to the base b of x". This means that, log_b 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,

=

-1

The exponential function and logarithmic function are inverse functions of each other, since

y = log_b x if and only if x = b^y.

If y = log₁₀ x = f(x), then x = 10^y and vice-versa.

If x = e^y then y = ln x and vice versa.

The shape of the logarithmic function y = ln x is graphically illustrated below.

Posted Date: 9/13/2012 6:06:50 AM | Location : United States

Ask an Expert

Related Discussions:- Logarithmic functions, Assignment Help, Ask Question on Logarithmic functions, Get Answer, Expert's Help, Logarithmic functions Discussions

Write discussion on Logarithmic functions
Your posts are moderated

Write your message here..

Related Questions

Calculate the total surface area which is exposed , A golf ball has a diame... A golf ball has a diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate the total surface area which is exposed to the surroundings assuming that the d

Word problems, please can you help me with word problems please can you help me with word problems

Example of inflection point-differential equation, Example of inflection po... Example of inflection point Determine the points of inflection on the curve of the function y = x 3 Solution The only possible inflexion points will happen where

Compute the value of the following limit, Compute the value of the followin... Compute the value of the following limit. Solution: Notice as well that I did say estimate the value of the limit.  Again, we will not directly compute limits in this sec

Fracshions, how do you do it how do you do it

Lcm method, lcm method of 648 lcm method of 648

How far is that person from the starting point, A person travels 10 miles d... A person travels 10 miles due north, 6 miles due west, 4 miles due north, and 12 miles due east. How far is that person from the initail state? a. 23 miles northeast b. 13 mi

Problem solving sequence: the operations, marianne took $100.00 to a store ... marianne took $100.00 to a store that was holding a no-tax sale. she bought a shirt for $24.99, sandals for $18.50, shorts for $16.49, and a beach bag for $21.69. how much did she

Find the average, The center of a national park is located at (0,0). A spec... The center of a national park is located at (0,0). A special nature preserve is bounded by by straight lines connecting the points A at (3,2), B at (5,1), C at (8,4) and D at (6,5)

Ordinary and partial differential equations, A differential equation is ter... A differential equation is termed as an ordinary differential equation, abbreviated through odes, if this has ordinary derivatives in it. Similarly, a differential equation is term