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SugarRainbow
 3 years ago
how to do log base 16 of 1/4 ?!?!?!?!
SugarRainbow
 3 years ago
how to do log base 16 of 1/4 ?!?!?!?!

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ivanmlerner
 3 years ago
Best 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:\[4^{2x}=4^{1}\] \[2x=1\rightarrow x=\frac{1}{2}\]

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

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0then what would i do how do you divide them?

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0or if i use what ivanmlerner did what would i do next?

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

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0but i can't use a calculator

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0what if i did it how ivanmlerner did it?

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

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0how did you get 1/2

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0wait nevermind i got it

SugarRainbow
 3 years ago
Best ResponseYou've already chosen the best response.0wait so what about something like log base 1/4 of 16?

cruffo
 3 years ago
Best ResponseYou've already chosen the best response.0you 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: \[\large \left(\frac{1}{4}\right)^x = 16\]
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