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AonZ
 3 years ago
Last question!!!
log 1/5 (25)
AonZ
 3 years ago
Last question!!! log 1/5 (25)

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

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

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

ParthKohli
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1yes, simplify numerator and denominator separately.

agent0smith
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1Just figure out what you multiply to \(5^{1}\) to get \(5^2.\)

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

AonZ
 3 years 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
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1@AonZ Change of bases.

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

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

agent0smith
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1But you get the point.

agent0smith
 3 years 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
 3 years 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
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.1Much better up there.

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

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

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

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

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

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

agent0smith
 3 years 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
 3 years 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
 3 years 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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