Question

Match each each equation equation with the correct solution.
2e^x - 1 = 0
Choose... -1.2345/ 0.2877 /0.2747 /0.6438/ -0.06931/ 1.5041

Answer 1

ok lets solve this
can be written as
2e^x=1

Answer 2

take ln (natural log) of both sides
ln(2e^x)=ln(1)

Answer 3

simplify the above
let me know what you get after this.

Answer 4

@brendas

Answer 5

write 2e^x-1=0 as
e^x=1/2
take log of both sites
ln(e^x)=ln(1/2)
using property of log
xln(e)=ln(1/2)
since ln(e)=1
x=ln(1/2)
now use your calculator

Answer 6

@brendas if you need help about this let me know.

Answer 7

i need help

Answer 8

ok
what you are unable to fallow in the above?

Answer 9

i dont get how to solve it

Answer 10

ok
can i write
2e^x-1=0
as
2e^x=1

reply

Answer 11

yes but where does the 0 go

Answer 12

opps:P

Answer 13

let me do it again
2e^x-1=0
add one to the both sides of equation

2e^x-1+1=0+1
2e^x=0+1
2e^x=1 (0+1 is equal to 1)

Answer 14

is it ok now ?

Answer 15

@brendas

Answer 16

yea better

Answer 17

ok so whats the next step

Answer 18

ok
now divide both sides by 2
\[\frac{2e^x}{2}=\frac{1}{2}\]
since 2/2=1 so
\[e^x=\frac{1}{2}\]

are you with me ?
are you getting these steps?

Answer 19

yea i get the step

Answer 20

ok now take natural log of both sides
\[\ln(e^x)=\ln(\frac{1}{2})\]
using property of log the the thing in exponents comes down and gets multiplied with log so x should come down
\[xln(e)=\ln(\frac{1}{2})\]

is it ok ?

Answer 21

am here im looking at the next step which i dont get now

Answer 22

it is the property of log that the exponent comes down and gets multiplied like
\[\log_{b}x^n=nlog_{b}x\]
is it ok now

Answer 23

im sorry but i just dont get the log parts!!!!! so whats my next step on the problem

Answer 24

this is the answer i get -2.3026

Answer 25

ok take a look on in your book about logs section.

we were at
\[xln(e)=\ln \frac{1}{2}\]

since ln(e)=1
\[x=\ln (\frac{1}{2})\]
got it ?

Answer 26

got a calculator?

Answer 27

yea

Answer 28

ok use it and find
ln(1/2)
let me know what you got?

Answer 29

@brendas you got it?

Answer 30

ok i found using calculator
\[x=-0.6931\]
this the solution
Best of Luck with rest of your studies.