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anonymous
 one year ago
What is the value of
anonymous
 one year ago
What is the value of

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DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2\[\log _{81}\left(3\right)=\frac{1}{4}\quad \left(\mathrm{Decimal:\quad }\:0.25\right)\]

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2Happy:) @EllenJaz17

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do you value that though? I have to show my work

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2\[\mathrm{Rewrite\:}3\mathrm{\:\in\:powerbase\:form:}\quad 3=81^{\frac{1}{4}}\] \[=\log _{81}\left(81^{\frac{1}{4}}\right)\] \[\mathrm{Apply\:the\:\log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)\] \[\log _{81}\left(81^{\frac{1}{4}}\right)=\frac{1}{4}\log _{81}\left(81\right)\] \[=\log _{81}\left(81\right)\frac{1}{4}\] \[\mathrm{Apply\:the\:\log\:rule}:\quad \log _a\left(a\right)=1\] \[\log _{81}\left(81\right)=1\] =1/4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\log_{81}(3)=x\iff 81^x=3\] so what you are trying to do is figure out how to write 3 as a power of 81 since \(\sqrt[4]{81}=3\) that tells you \[81^{\frac{1}{4}}=3\] and you have the power you are looking for

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so it's not 1/4 its 3?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0another easier example \[\log_7(49)=2\] because \(7^2=49\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no the answer is \(\frac{1}{4}\) let me write it again

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\huge \log_{81}(\color{red}x)=3\iff 81^{\color{red}x}=3\] you are trying to find \(\color{red}x\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you are looking for the power that you would raise 81 to to give you 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\log_2(8)=3\iff 2^3=8\] they say the same thing

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you should be able to switch back and forth quickly

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the only tricky part of this one was recognizing that 3 is the fourth root of 81

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0.sorry catching up was getting something to drink

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I prefer straight tequila, gets the job done quick lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no beer chaser? dang!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops do you get that \(2^5=32\) says the same thing as \(\log_2(32)=5\) ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would i apply that to find this value in my question?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so if you were trying to solve \[\log_2(32)=\color{red}x\] you would be trying to solve \[2^{\color{red}x}=32\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you have \[\log_{81}(3)=\color{red}x\] you have to solve \[81^{\color{red}x}=3\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since \(\sqrt[4]{81}=x\) that is the same think as saying \(81^{\frac{1}{4}}=3\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ooops i means "since \(\sqrt[4]{81}=3\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now you have the power you are looking for , that power is \(\frac{1}{4}\) therefore since \[81^{\frac{1}{4}}=3\] it is the same as saying \[\log_{81}(3)=\frac{1}{4}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok i kinda get it lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah it is confusing at first a simpler example is it clear that \(10^4=10,000\)?
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