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SugarRainbow

  • 3 years ago

how to do log base 16 of 1/4 ?!?!?!?!

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  1. ivanmlerner
    • 3 years ago
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    \[\log_{16}\frac{1}{4}=x \rightarrow 16^x=4^{-1}\]Put them in the same base:\[4^{2x}=4^{-1}\] \[2x=-1\rightarrow x=-\frac{1}{2}\]

  2. cruffo
    • 3 years ago
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    or use change of base formula... \[\log_{16} \left(\frac{1}{4}\right) = \frac{\log 0.25}{\log 16}\]

  3. SugarRainbow
    • 3 years ago
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    then what would i do how do you divide them?

  4. SugarRainbow
    • 3 years ago
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    or if i use what ivanmlerner did what would i do next?

  5. cruffo
    • 3 years ago
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    For the change of base formula, just use a calculator with a log key: log(0.25)/log(16) =

  6. SugarRainbow
    • 3 years ago
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    but i can't use a calculator

  7. SugarRainbow
    • 3 years ago
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    what if i did it how ivanmlerner did it?

  8. cruffo
    • 3 years ago
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    if you do it the way @ivanmlerner suggested, then you are done. By finding x, you found the value of the log, that is \[\log_{16} \left(\frac{1}{4}\right) = -\frac{1}{2}\]

  9. SugarRainbow
    • 3 years ago
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    wait so x is -1/2

  10. SugarRainbow
    • 3 years ago
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    how did you get -1/2

  11. SugarRainbow
    • 3 years ago
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    wait nevermind i got it

  12. SugarRainbow
    • 3 years ago
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    wait so what about something like log base 1/4 of 16?

  13. cruffo
    • 3 years ago
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    you would go about it the same way, basically. Asking what \(\log_{1/4} 16\) is equal to is the same as asking the question "what power do I raise \(\dfrac{1}{4}\) to to get \(16\)?" In math, that means solving the equation for x: \[\large \left(\frac{1}{4}\right)^x = 16\]

  14. SugarRainbow
    • 3 years ago
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    so 64?

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