Question

Need help understanding how to find all the roots of this equation

Answer 1

\[\ln x=(\log_{10} e)/(\log_{10} x)\]

Answer 2

multiply both side by \[\log_{10}x \] ?

Answer 3

i think its best to convert the logs to the same base

using the formula loga x = logb x / logb a

convert ln to log10

Answer 4

\[\ln x = \log_{10} x\] ? sorry the property and rules always mess me up. especially ln x and ln e and the others

Answer 5

\[\log_{e} x=\frac{ \log_{10}e }{ \log_{10}x }\]
starting it off right?

Answer 6

\[\log_{e} x+\log_{10} x=\log_{10}e \]

Answer 7

i dunno....

Answer 8

\[\log_{e} x=\log_{10} e-\log_{10} x\]
maybe this way?

Answer 9

Is this the question? \[\ln(x)=\frac{ \log_{10}e }{ \log_{10}x }\]

Answer 10

\[logx_{10} =logx_{e} /\log10_{e} \]

Answer 11

well the original in the book is\[\ln x=(\log_{10}e)/(\log_{10}x) \]

Answer 12

@Nameless substitute n solve u will get x=e

Answer 13

isnt \[\ln x=\log_{e} x\]
?

Answer 14

ya that's right

Answer 15

\[\ln(x)=\frac{ \log_{10}e }{ \log_{10}x }\]\[\ln(x)=\log_{x}e\]\[\ln(x)=\frac{ 1 }{ \ln(x) }\]\[(\ln(x))^{2}=1\]\[\ln(x)=\pm1\]\[x=e^{\pm1}\]

Answer 16

log base x of e = 1/ln(x)?

Answer 17

yep\[\log_{x}e=\frac{ 1 }{ \log_{e}x }=\frac{ 1 }{ \ln(x) }\]

Answer 18

so when you are dividing logs, the exponent in the denominator is set at the base and the exponent in the numerator is set as "x"?

Answer 19

as long as their the same base to begin with? sorry just trying to derive your \[\log_{x} e\]

Answer 20

This is one of the properties of logarithm.

Answer 21

quotient property?

Answer 22

\[\log_{a}b=\frac{ \log_{c}b }{ \log_{c}a }\]

Answer 23

\[\log_{c} \frac{ b }{ a }\]?

Answer 24

nope

Answer 25

By the way what grade are you?

Answer 26

im in my 2nd year of college

Answer 27

This must be simple for you.

Answer 28

i am desperately trying to understand these properties.

Answer 29

not really. or I wouldnt be asking for help :)

Answer 30

Did you know this property? \[\log_{a}b=\frac{ \log_{c}b }{ \log_{c}a }\]

Answer 31

kind of. i am just confused how you got it into the log base x of b form

Answer 32

or log base x of e

Answer 33

Did you know that property?
First answer me this

Answer 34

it is in my notes yes.. but a lot of times I have a hard time connecting actual problems to the properties.

Answer 35

ahh okay i see it now...

Answer 36

Thank you