Question

what is the method of finding domain and range of Log functions
like ln(2x-1)

Answer 1

well, 2x-1 shud not be equal to zero greater than zero and range is R

Answer 2

other than zero all the real number are included then...???

Answer 3

for what? range or domain

Answer 4

for range

Answer 5

zero is inc in range as x=1

Answer 6

i.e. 2x-1=1

Answer 7

sorry i am not getting it

Answer 8

log 1=0

Answer 9

then domain is from 1-+infinity

Answer 10

1to +infinity right..??

Answer 11

nope log 1/x = -log x so domain is R

Answer 12

ahan oka got it ... mean range will include zero as well as it is set w.. an domain will ve all real num xcpt zero.. right maha/?

Answer 13

dom = [1,infnty

Answer 14

range is for dependent variable right..??

Answer 15

oops i dint read ur comment properly...domain is ok from ur side @Maha_Chauhan

Answer 16

dom is from 1_+infinity and range is all real #'s rite?

Answer 17

You cannot take ln of anything <= 0.

So 2x - 1 > 0
x > 1/2. So the domain is (1/2, infinity)

The range is (-infinity, infinity).

y approaces -infinity when x = 1/2 and
y approaches +infinity when x approaches +infinity

Answer 18

how it can be 1/2..???

Answer 19

the point that i got is log's cant be of 0 and negative numbers.. right...??? @divu.mkr

Answer 20

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Answer 21

yep inside log it can't be zero or negative

Answer 22

then it becomes domain right..??

Answer 23

hmm

Answer 24

okay thanku so much

Answer 25

np

Answer 26

in a log if the function is \[x^{2}+y^{2}\how the domain will be obtained..??

Answer 27

log(A), ln(A) are all defined only when A > 0

Is the question, What is the domain of \[\Large \log(x ^{2} + y ^{2})\]?

Answer 28

yes @ranga

Answer 29

log(A) is defined ONLY for A > 0

So (x^2 + y^2) must be > 0.

But both x and y are squared. So whether they x and y are positive or negative x^2 and y^2 will always be > 0. The only exception is when BOTH x and y are 0. Then x^2 + y^2 will be 0 which is not defined for log function. x can be separately 0, y can be separately 0 but they both cannot be simultaneously 0.

So the domain is: x can be any real number including 0 but BOTH x and y cannot be simultaneously be 0.

Answer 30

thank you...@ranga

Answer 31

you are welcome.