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Log question. Is there a rule that can solve this?
\[\huge \log_{\frac{ 1 }{ a }} \frac{ 1 }{ n }\]
 one year ago
 one year ago
Log question. Is there a rule that can solve this? \[\huge \log_{\frac{ 1 }{ a }} \frac{ 1 }{ n }\]
 one year ago
 one year ago

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AonZBest ResponseYou've already chosen the best response.0
@agent0smith can you help with this?
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
Yeah i'm not sure what you want to do with it... you can change it into a couple of different forms?
 one year ago

yakzoBest ResponseYou've already chosen the best response.0
There is a formula for changing the base of the logarithm.
 one year ago

AonZBest ResponseYou've already chosen the best response.0
well il type full equation prove log a(x) = log 1/2 (x)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
use : \(\huge \log_ab=\dfrac{\log b}{\log a}\)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
u sure, this is the Q ? prove log a(x) = log 1/2 (x)
 one year ago

AonZBest ResponseYou've already chosen the best response.0
wait my bad LOL log a(x) = log 1/a (x)
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
right, use the property i gave on RIGHT side.
 one year ago

AonZBest ResponseYou've already chosen the best response.0
dw:1360928591721:dw these cancel right?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
simplify both numerator and denominator. and  log x = log(1/x) was unnecessary and no, not directly.
 one year ago

AonZBest ResponseYou've already chosen the best response.0
how else do i do it then??
 one year ago

AonZBest ResponseYou've already chosen the best response.0
oh so the negatives cancel?
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
yesh, now negatives can cancel.
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
again apply that property on what you have...
 one year ago

hartnnBest ResponseYou've already chosen the best response.2
\(\huge \dfrac{\log b}{\log a}=\log_ab\)
 one year ago

AonZBest ResponseYou've already chosen the best response.0
yes i can see how the equal each other now :)
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
\[\log_{a} x = \log_{\frac{ 1 }{ a }} x\] Use the log rule on the right side \[\log_{\frac{ 1 }{ a }} x = \frac{ \log_{a} x }{ \log_{a} \frac{ 1 }{ a } } = \frac{ \log_{a} x }{ \log_{a} a ^{1}}= \frac{ \log_{a} x }{ \log_{a} a} = \frac{ \log_{a} x }{1}\]
 one year ago

agent0smithBest ResponseYou've already chosen the best response.1
moved the negatives, makes it easier to follow. \[\log_{\frac{ 1 }{ a }} x = \frac{  \log_{a} x }{ \log_{a} \frac{ 1 }{ a } } = \frac{ \log_{a} x }{ \log_{a} a ^{1}}= \frac{ \log_{a} x }{ \log_{a} a} = \frac{ \log_{a} x }{1}\]
 one year ago

AonZBest ResponseYou've already chosen the best response.0
ahh ok thanks to all of you :)
 one year ago
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