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

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AonZ
 2 years ago
Best ResponseYou've already chosen the best response.0@agent0smith can you help with this?

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah i'm not sure what you want to do with it... you can change it into a couple of different forms?

yakzo
 2 years ago
Best ResponseYou've already chosen the best response.0There is a formula for changing the base of the logarithm.

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

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

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

AonZ
 2 years ago
Best ResponseYou've already chosen the best response.0wait my bad LOL log a(x) = log 1/a (x)

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2right, use the property i gave on RIGHT side.

AonZ
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1360928591721:dw these cancel right?

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

AonZ
 2 years ago
Best ResponseYou've already chosen the best response.0how else do i do it then??

AonZ
 2 years ago
Best ResponseYou've already chosen the best response.0oh so the negatives cancel?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2yesh, now negatives can cancel.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2again apply that property on what you have...

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.2\(\huge \dfrac{\log b}{\log a}=\log_ab\)

AonZ
 2 years ago
Best ResponseYou've already chosen the best response.0yes i can see how the equal each other now :)

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1\[\log_{a} x = \log_{\frac{ 1 }{ a }} x\] Use the log rule on the right side \[\log_{\frac{ 1 }{ a }} x = \frac{ \log_{a} x }{ \log_{a} \frac{ 1 }{ a } } = \frac{ \log_{a} x }{ \log_{a} a ^{1}}= \frac{ \log_{a} x }{ \log_{a} a} = \frac{ \log_{a} x }{1}\]

agent0smith
 2 years ago
Best ResponseYou've already chosen the best response.1moved the negatives, makes it easier to follow. \[\log_{\frac{ 1 }{ a }} x = \frac{  \log_{a} x }{ \log_{a} \frac{ 1 }{ a } } = \frac{ \log_{a} x }{ \log_{a} a ^{1}}= \frac{ \log_{a} x }{ \log_{a} a} = \frac{ \log_{a} x }{1}\]

AonZ
 2 years ago
Best ResponseYou've already chosen the best response.0ahh ok thanks to all of you :)
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