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AonZBest ResponseYou've already chosen the best response.0
check the identity by evaluating...
 one year ago

AonZBest ResponseYou've already chosen the best response.0
\[\huge \log_{\frac{ 1 }{ 5 }}25 \]
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
use the same property i gave for last Q
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
\(\frac{1}{5} = 5^{1}\). What would you multiply to that to get \(5^2\)?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
yes, simplify numerator and denominator separately.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
\[\large \log_{\frac{ 1 }{ 5 }} 5 = \frac{ \log_{5} 25 }{ \log_{5}\frac{ 1 }{ 5}} = \frac{ \log_{5} 5^2 }{ \log_{5} 5^{1}}\]
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Just figure out what you multiply to \(5^{1}\) to get \(5^2.\)
 one year ago

AonZBest ResponseYou've already chosen the best response.0
ahh @agent0smith explained it pretty good :)
 one year ago

AonZBest ResponseYou've already chosen the best response.0
@agent0smith How did you get the base to be 5? Like all of them?
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
Not sure what you mean... I just used base 5 because it makes it easy to solve.
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
@AonZ Change of bases.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
you can choose any base for using that property,e,5,10,... thats why its unspecified in the property
 one year ago

AonZBest ResponseYou've already chosen the best response.0
so if you use change of base rule you can choose ANY base?
 one year ago

AonZBest ResponseYou've already chosen the best response.0
wow i reckon i understand logs a lot better now :P
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
^ correct @ParthKohli shouldn't it be "figure out what power you need to raise 5^1 to, to get 25" as opposed to "Just figure out what you multiply to 5^−1 to get 5^2"?
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
But you get the point.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
Ah okay, cos i was wondering how this helps:\[5^{1} \times 5^3 = 25\]compared to this \[(5^{1})^{2}=25\]
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
@AonZ you could also do it this way (but it makes it a bit more difficult): \[ \large \log_{\frac{ 1 }{ 5 }} 5 = \frac{ \log_{25} 25 }{ \log_{25}\frac{ 1 }{ 5}} = \frac{1 }{ \log_{25} 25^{0.5}}\]
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
or simply \(\huge \log_{\frac{ 1 }{ 5 }} 5 = \frac{ \log_{} 5 }{ \log_{}\frac{ 1 }{ 5}} \)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
Much better up there.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
\(\huge \log_{\frac{ 1 }{ 5 }} 25 = \frac{ \log_{} 25 }{ \log_{}\frac{ 1 }{ 5}}\)
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
^ that works fine, but requires a calculator.
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
\(\huge \log_{\frac{ 1 }{ 5 }} 25 = \frac{ \log_{} 25 }{ \log_{}\frac{ 1 }{ 5}}= \frac{ \log_{} 5^2 }{ \log_{}\frac{ 1 }{ 5}}\)
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
\[\dfrac{\log _5 5^2}{\log _5 5^{1}} = \]
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
I'm assuming @hartnn is using base 10...
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
does not matter what base i use, by default its 10
 one year ago

ParthKohliBest ResponseYou've already chosen the best response.1
You can use change of base too.
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
\[ \frac{ \log_{} 25 }{ \log_{}\frac{ 1 }{ 5}} \] I mean, how are you solving this w/o changing base again, or using a calculator?
 one year ago

hartnnBest ResponseYou've already chosen the best response.1
\(\huge \log_{\frac{ 1 }{ 5 }} 25 = \frac{ \log_{} 25 }{ \log_{}\frac{ 1 }{ 5}}= \frac{ \log_{} 5^2 }{ \log_{}\frac{ 1 }{ 5}}=\dfrac{2 \log 5}{1 \log 5}=2\)
 one year ago

agent0smithBest ResponseYou've already chosen the best response.2
Oh you're simplifying to \[ \frac{ \log_{} 25 }{ \log_{}\frac{ 1 }{ 5}} = \frac{ 2 \log5 }{ \log5 }\]
 one year ago
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