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

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

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

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

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

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.2\[\large \log_{\frac{ 1 }{ 5 }} 5 = \frac{ \log_{5} 25 }{ \log_{5}\frac{ 1 }{ 5}} = \frac{ \log_{5} 5^2 }{ \log_{5} 5^{1}}\]

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

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

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

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.2Not sure what you mean... I just used base 5 because it makes it easy to solve.

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

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

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

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

agent0smith
 one year ago
Best 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"?

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

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.2Ah okay, cos i was wondering how this helps:\[5^{1} \times 5^3 = 25\]compared to this \[(5^{1})^{2}=25\]

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.2@AonZ you could also do it this way (but it makes it a bit more difficult): \[ \large \log_{\frac{ 1 }{ 5 }} 5 = \frac{ \log_{25} 25 }{ \log_{25}\frac{ 1 }{ 5}} = \frac{1 }{ \log_{25} 25^{0.5}}\]

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

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

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

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.2^ that works fine, but requires a calculator.

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

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

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.2I'm assuming @hartnn is using base 10...

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

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

agent0smith
 one year ago
Best 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?

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

agent0smith
 one year ago
Best ResponseYou've already chosen the best response.2Oh you're simplifying to \[ \frac{ \log_{} 25 }{ \log_{}\frac{ 1 }{ 5}} = \frac{ 2 \log5 }{ \log5 }\]
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