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GOODMAN
Group Title
Have a few problems I was stuck on.
1)log_9(x+4)+log_9(x4)=1
2)Sqrt(3x2)sqrt(x)=1
 2 years ago
 2 years ago
GOODMAN Group Title
Have a few problems I was stuck on. 1)log_9(x+4)+log_9(x4)=1 2)Sqrt(3x2)sqrt(x)=1
 2 years ago
 2 years ago

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GregTheo Group TitleBest ResponseYou've already chosen the best response.0
First combine the logs ( addition of log is multiplication) log(x+4) + log(x4) = Log ((x+4)/(x4)) raise everything from base 9 for part one, doing this cancels the log because they are inverse functions and 9^1 is just 9 resulting in (x+4)(x4) = 9 distribute x^2 16 = 9 x^2 = 25 x= + or 5
 2 years ago

GregTheo Group TitleBest ResponseYou've already chosen the best response.0
typo, the log product should read log ((X+4)(x4))
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
ok lets solve it since \[\Large \log(a)+\log(b)=\log(ab)\] (addition changes to multiplication \[\Large \log _{9}((x+4)(x4))=1\] since \[\Large a^2b^2=(a+b)(ab)\] so \[\Large \log _{9}(x^216)=1\]
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
Yes, I got as far as @sami21 But got stuck. I knew the answer was 5. Didnt know how to get it.
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
so now we can cgange the log by change of bass formula
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
Hmm..thats where i got stuck. How do you do that?
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
\[\Large \log _{a}(b)=\frac{\ln(a)}{\ln{b}}\]
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
it is upto use to change it to any base .i used natural log whose base is e
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
Hmm...i think i get it.
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
I had another one similar to it: 7^(5x2)=5^(3x)
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
I know you have to log both sides.
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
yes take ln of both sides
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
then use property \[\Large \log _{a}(b)^n=nlog _{a}b\] which means exponents gets down and gets multiplied !
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
let me do the your question now using above property
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
take ln of both sides\[\Large \ln(7)^{5x2}=\ln(5)^{3x}\] so using the above mentioned property \[\Large (5x2)\ln(7)=(3x)\ln(5)\]
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
now use calculator to find values of ln7 and ln5
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
ln7=1.946 ln5=1.609
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
ln(7)=1.94 ln(5)=1.60 (5x2)*(1.69)=(3x)1.609
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
can you solve this !!
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
Yesss. I can take it from there, thank you so much! And the last one, so sorry, is b on the question.
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
a typo ! correct is (5x2)*(1.94)=(3x)1.609
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
ok. u mean this \[\Large \sqrt{3x2}\sqrt{x}=1\] ??
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
ok taking square of both sides
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
we have \[\Large (\sqrt{3x2}\sqrt{x})^2=1^2\] using \[\Large (ab)^2=a^2+b^22ab\] we have \[\Large ((3x2)+x2\sqrt{3x2}\sqrt{x})=1\]
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
Sorry, it was 3x3
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
Itsokay i will pretend the 2 was really 3
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
its ok :) i am notorious for typo mistakes ask anyone here :P
 2 years ago

sami21 Group TitleBest ResponseYou've already chosen the best response.1
have a look at here http://www.wolframalpha.com/input/?i=solve%28sqrt%283x3%29sqrt%28x%29%3D1%29 its quite difficult to type :P
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
Wow, thats good enough! Thank you soo much for your help. I learned a lot!
 2 years ago

GOODMAN Group TitleBest ResponseYou've already chosen the best response.0
Also, thank you too @GregTheo
 2 years ago

muhammad9t5 Group TitleBest ResponseYou've already chosen the best response.0
\[\sqrt(3x2)\sqrt(x)=1\] add \[\sqrt(x)\] in both sides
 2 years ago
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