Question

What is the range of f(x) = log7x?

Answer 1

so is it all reals

Answer 2

yep

Answer 3

domain is x>0, range is R

Answer 4

ok

Answer 5

Find the zero(s) of the function f(x) = log5x.
Hint: The zeros are all the values of x when f(x) = 0.

Answer 6

\[\log 5x=0\]\[10^{\log(5x)}=10^0\]\[5x=1\]\[x=\frac{1}{5}\]

Answer 7

so the zeros are 1/5

Answer 8

There is no value of log(x) that gives 0. No exponent to which any base can be raised that gives 0.

Answer 9

@telliott99 incorrect. \[\log 5(\frac{1}{5})=\log 1=0\]because.\[1=10^0\]

Answer 10

so the answer will be 0

Answer 11

?

Answer 12

do you understand what the "zero" of a function means?

Answer 13

yes

Answer 14

ok

Answer 15

so what is the zero of log (5x) ?

Answer 16

1

Answer 17

no

Answer 18

the zero of a function f(x) is the value x, such that f(x)=0

Answer 19

log (5*1)=log 5 does not equal zero. so x=1 is not a "zero"

Answer 20

so there is no solution

Answer 21

?

Answer 22

@eseidl sorry my bad
but No exponent to which any base can be raised that gives 0.
so no x that log(x) = 0

Answer 23

Again! I mean no p where e^p = 0

Answer 24

@telliott99 your misunderstanding the nature of the logarithm. y=logx
take "antilog" of both sides. \[10^y=x\]set y=0.\[10^0=x\]\[x=1\]what's the problem?

Answer 25

I agree that there is no p such that \[e^p=0\]but this doesn't imply that there is no x such that\[\log_{a}x=0 \]If fact x=1 will give \[\log_{a}1=0 \]for any base a. Because,\[1=a^0\]

Answer 26

Just tired and typing the wrong things. Apologies for causing confusion.