Click to Chat

1800-2000-838

+91-120-4616500

CART 0

• 0

MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
`        throw some light on logrithmic functions`
7 years ago

105 Points
```										Dear Yazdan,
THE LOGARITHMIC FUNCTION WITH BASE b  is the function
y  =  logb x.
b is normally a number greater than 1  (although it need only  be greater than 0 and not equal to 1).  The  function is defined for all x > 0.  Here is its graph for any base b.

Note the following:
•  For any base, the x-intercept is  1.  Why?

The logarithm of 1 is 0.  y = logb1 = 0.
•  The graph passes through the point (b, 1).   Why?
The logarithm of the base is 1.  logbb = 1.

•
The graph is below the x-axis -- the logarithm is negative -- for

0 < x < 1.

Which numbers are those  that have negative logarithms?

Proper fractions.

•
The function is defined only for positive values of x.

logb(−4), for example, makes no sense.  Since b is always positive, no power of b can produce a negative number.

•  The range of the function is all real numbers.
•  The negative y-axis is a vertical asymptote (Topic 18).
Example 1.   Translation of axes.   Here is the graph of the natural logarithm,  y = ln x  (Topic 20).

And here is the graph of   y = ln (x − 2) -- which is its translation 2 units to the right.

The x-intercept has moved from 1 to 3.  And the vertical asymptote has moved from 0 to 2.
Problem 1.   Sketch the graph of y = ln (x + 3).

This is a translation 3 units to the left.   The x-intercept has moved from 1 to −2.  And the vertical asymptote has moved from 0 to −3.
All the best.
Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.

Suryakanth –IITB

```
7 years ago
Think You Can Provide A Better Answer ?

## Other Related Questions on Algebra

View all Questions »
• Complete JEE Main/Advanced Course and Test Series
• OFFERED PRICE: Rs. 15,900
• View Details