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recon14193 Group TitleBest ResponseYou've already chosen the best response.0
\[\log_{a}x+\log_{a}x2=\log_{a}x+4 \]\ \[\log_{a}x(x2)=\log_{a}x+4\] that is my work so far I do not know how to convert to exponential
 one year ago

recon14193 Group TitleBest ResponseYou've already chosen the best response.0
I am wondering if I divide by \[\log_{a}x+4\] and then have it equal to zero which means my final answer is just 1
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
assuming the right hand side is \(\log_a(x+4)\) then your last job is to solve \[x(x2)=x+4\]
 one year ago

recon14193 Group TitleBest ResponseYou've already chosen the best response.0
so the logs just drop out
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
log is a "one to one function" so if \[\log(A)=\log(B)\] then \(A=B\)
 one year ago

recon14193 Group TitleBest ResponseYou've already chosen the best response.0
ok I guess but I dont really understand
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
ok suppose instead of log, you had \[f(x)=2x+4\]
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
if you were told that \[2a+4=2b+4\] then you would know that \(a=b\) right?
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
it is the same with the log if \(\log(x)=\log(y)\) then you know \(x=y\)
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
in other words, as in your example, the only way for \(\log(x^22x)\) to be equal to \(\log(x+4)\) is if \(x^22x=x+4\)
 one year ago

recon14193 Group TitleBest ResponseYou've already chosen the best response.0
oh I see now so if i understand correctly it is because we know they must be equal that the fact that it is a log of each does not matter because no matter what they yield the same result
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yes, exactly
 one year ago

recon14193 Group TitleBest ResponseYou've already chosen the best response.0
Thank you I appreciate your help
 one year ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
if i know \(\log(x)=\log(5)\) then i know that \(x=5\) i cannot be anything else
 one year ago
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