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wcaprar

  • 4 years ago

How are e and ln related? If I have e^(4x) and x=ln2, where can I go from there? (This is calc related)

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  1. JamesJ
    • 4 years ago
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    f(x) = e^x and g(x) = ln(x) are inverse functions of each other: \[ f(g(x)) = e^{\ln x} = x\] \[ g(f(x)) = \ln(e^x) = x \]

  2. JamesJ
    • 4 years ago
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    Therefore, if \( x = \ln 2 \), then \[ 4x = 4 \ln 2 = \ln(2^4) = \ln(16) \] and hence \[ e^{4x} = ... what? \]

  3. wcaprar
    • 4 years ago
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    It's equal to 16, then?

  4. JamesJ
    • 4 years ago
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    Yes

  5. wcaprar
    • 4 years ago
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    Awesome! Thanks!

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