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

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\[\log_{16}\frac{1}{4}=x \rightarrow 16^x=4^{-1}\]Put them in the same base:\[4^{2x}=4^{-1}\] \[2x=-1\rightarrow x=-\frac{1}{2}\]
or use change of base formula... \[\log_{16} \left(\frac{1}{4}\right) = \frac{\log 0.25}{\log 16}\]
then what would i do how do you divide them?

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or if i use what ivanmlerner did what would i do next?
For the change of base formula, just use a calculator with a log key: log(0.25)/log(16) =
but i can't use a calculator
what if i did it how ivanmlerner did it?
if you do it the way @ivanmlerner suggested, then you are done. By finding x, you found the value of the log, that is \[\log_{16} \left(\frac{1}{4}\right) = -\frac{1}{2}\]
wait so x is -1/2
how did you get -1/2
wait nevermind i got it
wait so what about something like log base 1/4 of 16?
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: \[\large \left(\frac{1}{4}\right)^x = 16\]
so 64?

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