- #1

- 160

- 9

## Homework Statement

h(x)=e^(2x)-2

a)Write down the Dh

b)Solve the equation e^(2x)-2=e^x

## Homework Equations

## The Attempt at a Solution

a)x∈ℝ[/B]

e^(2x)-2=e^x

((e^x)^2)-e^x-2=0

I don't know what to do here:

Last edited:

- Thread starter Jaco Viljoen
- Start date

- #1

- 160

- 9

h(x)=e^(2x)-2

a)Write down the Dh

b)Solve the equation e^(2x)-2=e^x

a)x∈ℝ[/B]

e^(2x)-2=e^x

((e^x)^2)-e^x-2=0

I don't know what to do here:

Last edited:

- #2

Mark44

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Move the e## Homework Statement

h(x)=e^(2x)-2

a)Write down the Dh

b)Solve the equation e^(2x)-2=e^x

## Homework Equations

## The Attempt at a Solution

a)x∈ℝ[/B]

e^(2x)-2=e^x

((e^x)^2)-2=e^x

I don't know what to do here:

- #3

- 160

- 9

Thank you,

I initially did this but how do I factor e^(x2)

I also considered adding a ln to both sides to get rid of the e on both sides but the -2 is the problem.

- #4

Ray Vickson

Science Advisor

Homework Helper

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You need to go back and review the laws of exponents. How does ##e^{2x}## relate to ##e^x##? Surely you must have had such material already, or else you would not have been asked to do this problem.

Thank you,

I initially did this but how do I factor e^(x2)

I also considered adding a ln to both sides to get rid of the e on both sides but the -2 is the problem.

- #5

Mark44

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What you wrote in post #1 should be something of a hint.Hi Mark,

Thank you,

I initially did this but how do I factor e^(x2)

Jaco Viljoen said:e^(2x)-2=e^x

((e^x)^2)-e^x-2=0

If you have terms added together, taking the log is not any help.Jaco Viljoen said:I also considered adding a ln to both sides to get rid of the e on both sides but the -2 is the problem.

- #6

- 160

- 9

((e^x)^2)-2=e^x

(k^2)-k-2=0 k=e^x

(k+1)(k-2)=0

k=-1 or k=+2

e^x=2

lne^x=ln2

x=ln2

(k^2)-k-2=0 k=e^x

(k+1)(k-2)=0

k=-1 or k=+2

e^x=2

lne^x=ln2

x=ln2

- #7

Mark44

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This is correct, but you should say why your are discarding the other value of k.((e^x)^2)-2=e^x

(k^2)-k-2=0 k=e^x

(k+1)(k-2)=0

k=-1 or k=+2

e^x=2

lne^x=ln2

x=ln2

- #8

- 21

- 2

b)The solution can go through this path: (e^x)^2-e^x-2=0

If e^x=y i) then the equation is transformed like that: y^2-y-2=0

then the solutions are y=(1±3)/2 and from i) we get e^x=(1±3)/2 BUT since the function e^x can only give positive results for x∈ℝ the only acceptable solution would be the one with the +. So e^x=2 ⇔ x=ln2, there you go friend I hope this helps :)

- #9

Mark44

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The OP has already gotten all of this.ℝ

b)The solution can go through this path: (e^x)^2-e^x-2=0

If e^x=y i) then the equation is transformed like that: y^2-y-2=0

then the solutions are y=(1±3)/2 and from i) we get e^x=(1±3)/2 BUT since the function e^x can only give positive results for x∈ℝ the only acceptable solution would be the one with the +. So e^x=2 ⇔ x=ln2, there you go friend I hope this helps :)

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