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ivanmlernerBest ResponseYou've already chosen the best response.1
\[\log_{16}\frac{1}{4}=x \rightarrow 16^x=4^{1}\]Put them in the same base:\[4^{2x}=4^{1}\] \[2x=1\rightarrow x=\frac{1}{2}\]
 one year ago

cruffoBest ResponseYou've already chosen the best response.0
or use change of base formula... \[\log_{16} \left(\frac{1}{4}\right) = \frac{\log 0.25}{\log 16}\]
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
then what would i do how do you divide them?
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
or if i use what ivanmlerner did what would i do next?
 one year ago

cruffoBest ResponseYou've already chosen the best response.0
For the change of base formula, just use a calculator with a log key: log(0.25)/log(16) =
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
but i can't use a calculator
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
what if i did it how ivanmlerner did it?
 one year ago

cruffoBest ResponseYou've already chosen the best response.0
if you do it the way @ivanmlerner suggested, then you are done. By finding x, you found the value of the log, that is \[\log_{16} \left(\frac{1}{4}\right) = \frac{1}{2}\]
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
wait so x is 1/2
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
how did you get 1/2
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
wait nevermind i got it
 one year ago

SugarRainbowBest ResponseYou've already chosen the best response.0
wait so what about something like log base 1/4 of 16?
 one year ago

cruffoBest ResponseYou've already chosen the best response.0
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: \[\large \left(\frac{1}{4}\right)^x = 16\]
 one year ago
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