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3psilon

  • 3 years ago

I am terrible with Logs plz help

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  1. 3psilon
    • 3 years ago
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    \[f(x) = \log_{3}(\sqrt(x) + 3 \ \]

  2. 3psilon
    • 3 years ago
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    Log base 3 square root x plus 3

  3. 3psilon
    • 3 years ago
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    How do you find the inverse of this/

  4. anonymous
    • 3 years ago
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    start with the fact that \(\log_3(\sqrt{x})=\frac{1}{2}\log_3(x)\)

  5. anonymous
    • 3 years ago
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    is it the log of the whole thing?

  6. 3psilon
    • 3 years ago
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    No just log base 3 square root x

  7. anonymous
    • 3 years ago
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    i mean is it \[f(x)=\log_3(\sqrt{x}+3)\] or \[f(x)=\log_3(\sqrt{x})+3\]

  8. 3psilon
    • 3 years ago
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    2nd one

  9. anonymous
    • 3 years ago
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    ok then start with \[f(x)=\frac{1}{2}\log_3(x)+3\]

  10. anonymous
    • 3 years ago
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    we can do the usual trick of writing \[y=\frac{1}{2}\log_3(x)+3\]then \[x=\frac{1}{2}\log_3(y)+3\] and solve for \(y\)

  11. anonymous
    • 3 years ago
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    you need the steps?

  12. 3psilon
    • 3 years ago
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    Yes please . I always get confused when there's stuff like log base 3

  13. anonymous
    • 3 years ago
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    1) subtract 3 2) multiply by 2 3) raise 3 to everything

  14. anonymous
    • 3 years ago
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    \[x=\frac{1}{2}\log_3(y)+3\] \[x-3=\frac{1}{2}\log_3(y)\] \[2x-6=\log_3(y)\] \[3^{2x-6}=y\]

  15. anonymous
    • 3 years ago
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    last step because \[\log_b(y)=x\iff b^x=y\]

  16. 3psilon
    • 3 years ago
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    Ohhh!!! Thank you so much !

  17. anonymous
    • 3 years ago
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    yw

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