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3psilon Group Title

I am terrible with Logs plz help

  • one year ago
  • one year ago

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  1. 3psilon Group Title
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    \[f(x) = \log_{3}(\sqrt(x) + 3 \ \]

    • one year ago
  2. 3psilon Group Title
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    Log base 3 square root x plus 3

    • one year ago
  3. 3psilon Group Title
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    How do you find the inverse of this/

    • one year ago
  4. satellite73 Group Title
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    start with the fact that \(\log_3(\sqrt{x})=\frac{1}{2}\log_3(x)\)

    • one year ago
  5. satellite73 Group Title
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    is it the log of the whole thing?

    • one year ago
  6. 3psilon Group Title
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    No just log base 3 square root x

    • one year ago
  7. satellite73 Group Title
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    i mean is it \[f(x)=\log_3(\sqrt{x}+3)\] or \[f(x)=\log_3(\sqrt{x})+3\]

    • one year ago
  8. 3psilon Group Title
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    2nd one

    • one year ago
  9. satellite73 Group Title
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    ok then start with \[f(x)=\frac{1}{2}\log_3(x)+3\]

    • one year ago
  10. satellite73 Group Title
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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 \(y\)

    • one year ago
  11. satellite73 Group Title
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    you need the steps?

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

    • one year ago
  13. satellite73 Group Title
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    1) subtract 3 2) multiply by 2 3) raise 3 to everything

    • one year ago
  14. satellite73 Group Title
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    \[x=\frac{1}{2}\log_3(y)+3\] \[x-3=\frac{1}{2}\log_3(y)\] \[2x-6=\log_3(y)\] \[3^{2x-6}=y\]

    • one year ago
  15. satellite73 Group Title
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    last step because \[\log_b(y)=x\iff b^x=y\]

    • one year ago
  16. 3psilon Group Title
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    Ohhh!!! Thank you so much !

    • one year ago
  17. satellite73 Group Title
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    yw

    • one year ago
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