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anonymous

  • 5 years ago

Evaluate the following expressions. Your answers must be exact and in simplest form. lne^-11=? e^(ln4)=? e^(lnsqrt(3))=? ln(1/(e^2))=? i would like to know the steps please:)

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  1. anonymous
    • 5 years ago
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    \[ln(e^x)=x\] so \[ln(e^{-11})=-11\]

  2. anonymous
    • 5 years ago
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    similarly \[e^{ln(x)}=x\] so \[e^{ln(4)}=4\]

  3. anonymous
    • 5 years ago
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    and \[e^{ln(\sqrt{3})}=\sqrt{3}\]

  4. anonymous
    • 5 years ago
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    for the last one, \[ln(\frac{1}{x})=-ln(x)\] so \[ln(\frac{1}{e^2})=-ln(e^2)=-2\]

  5. anonymous
    • 5 years ago
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    btw \[ln(\frac{a}{b})=ln(a)-ln(b)\]so \[ln(\frac{1}{b})=ln(1)-ln(b)=-ln(b)\]because \[ln(1)=0\]

  6. anonymous
    • 5 years ago
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    thank you !:)

  7. anonymous
    • 5 years ago
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    welcome. hope it is clear!

  8. anonymous
    • 5 years ago
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    oh yea def going in my notes lol :D

  9. anonymous
    • 5 years ago
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    notes? ;)

  10. anonymous
    • 5 years ago
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    yea so i can remember them and cram them in my head hahaha

  11. anonymous
    • 5 years ago
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    well its easy just gotta remember haha

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spraguer (Moderator)
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