1 / 7

Logarithmic Functions

Logarithmic Functions. Exponentiation: The third power of some number ‘b’ is the product of 3 factors of ‘b’. More generally, raising ‘b’ to the n-th power (n is a natural number) is done by multiplying n factors. The idea of logarithms is to reverse the operation of exponentiation.

nuala
Download Presentation

Logarithmic Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Logarithmic Functions

  2. Exponentiation: The third power of some number ‘b’ is the product of 3 factors of ‘b’. More generally, raising ‘b’ to the n-th power (n is a natural number) is done by multiplying n factors. The idea of logarithms is to reverse the operation of exponentiation. Definition: If b≠1 and ‘y’ are any two positive real numbers then there exists a unique real number ‘x’ satisfying the equation bx = y. This x is said to be the logarithm of y to the base b and is written as Logb y = x

  3. Thus log3 9 = 2 since 32 = 9 log6 216 = 3 since 63 = 216 log10 0.01 = -2 since 10-2 = 0.01 Similarly x0 = 1 implies that logx 1 = 0 Note: • Since the exponential function value can never be zero, we can say that logarithm of zero is undefined. 2. Similarly, logarithmic function is not defined for negative values.

  4. Types of logarithms: • logarithms to base 10 are called common logarithms • logarithms to base 2 are called binary logarithms • logarithms to base ‘e’ are called natural logarithms • Identities:

  5. Sol: Given that

  6. y Graph: y = x (0 , 1) y = ex y = loge x x (1 , 0)

More Related