- #1

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^{x}

f{g(x)} = ln e

^{x}= x; not an issue

g{f(x)}= e

^{ln x}= ???? (answer for this) f(x) and g(x) are inverse of each other.

how to solve the problem algebraically.

- Thread starter sphyics
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- #1

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f{g(x)} = ln e

g{f(x)}= e

how to solve the problem algebraically.

- #2

Hootenanny

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You answered the question yourself:^{x}

f{g(x)} = ln e^{x}= x; not an issue

g{f(x)}= e^{ln x}= ???? (answer for this) f(x) and g(x) are inverse of each other.

how to solve the problem algebraically.

f(x) and g(x) are inverse of each other.

- #3

- 102

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g{f(x)}= eYou answered the question yourself:

- #4

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What does it mean that f and g are inverses of eachother??

- #5

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I suggest trying to prove it for yourself first. If you really can't, I've "spoilered" a proof below. It sounds like you may want to go back and brush up on some of your fundamentals.g{f(x)}= e^{lnx}= ???? how to solve this equation algebraically and come to a solution..

[tex]\ln y = \ln e^{\ln x}[/tex]

[tex]\ln y = \ln x[/tex] (by the power rule of exponential functions, since ln e = 1)

[tex]y=x=e^{\ln x}[/tex]

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- #6

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OMG i was perfect till ln y = ln x; after that i confused myself over if ln y = ln x; does that imply y = x, now i can see the perfect picture, thanks very much for shedding light over the darkness my ignorance :)I suggest trying to prove it for yourself first. If you really can't, I've "spoilered" a proof below. It sounds like you may want to go back and brush up on some of your fundamentals.

[tex]\ln y = \ln e^{\ln x}[/tex]

[tex]\ln y = \ln x[/tex] (by the power rule of exponential functions, since ln e = 1)

[tex]y=x=e^{\ln x}[/tex]

Last edited:

- #7

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g{f(x)} = f{g(x)}, and both are one to one, hence inverse of each other.What does it mean that f and g are inverses of eachother??

- #8

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Algebraic Solution ??

OK

Let the solution be called "c"

e^(Ln x) = c

Take the Ln of both sides

Ln [ e^(Ln x) ] = Ln c

Use the Power Rule for Logs to get

Ln x Ln e = Ln c

but Ln e = 1 so

Ln x = Ln c

thus

c = x

OK

Let the solution be called "c"

e^(Ln x) = c

Take the Ln of both sides

Ln [ e^(Ln x) ] = Ln c

Use the Power Rule for Logs to get

Ln x Ln e = Ln c

but Ln e = 1 so

Ln x = Ln c

thus

c = x

Last edited:

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