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

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GregTheoBest 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
 one year ago

GregTheoBest ResponseYou've already chosen the best response.0
typo, the log product should read log ((X+4)(x4))
 one year ago

sami21Best 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 \[\Large \log _{9}(x^216)=1\]
 one year ago

GOODMANBest 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.
 one year ago

sami21Best ResponseYou've already chosen the best response.1
so now we can cgange the log by change of bass formula
 one year ago

GOODMANBest ResponseYou've already chosen the best response.0
Hmm..thats where i got stuck. How do you do that?
 one year ago

sami21Best ResponseYou've already chosen the best response.1
\[\Large \log _{a}(b)=\frac{\ln(a)}{\ln{b}}\]
 one year ago

sami21Best 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
 one year ago

GOODMANBest ResponseYou've already chosen the best response.0
Hmm...i think i get it.
 one year ago

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

GOODMANBest ResponseYou've already chosen the best response.0
I know you have to log both sides.
 one year ago

sami21Best ResponseYou've already chosen the best response.1
yes take ln of both sides
 one year ago

sami21Best 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 !
 one year ago

sami21Best ResponseYou've already chosen the best response.1
let me do the your question now using above property
 one year ago

sami21Best 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 \[\Large (5x2)\ln(7)=(3x)\ln(5)\]
 one year ago

sami21Best ResponseYou've already chosen the best response.1
now use calculator to find values of ln7 and ln5
 one year ago

sami21Best ResponseYou've already chosen the best response.1
ln(7)=1.94 ln(5)=1.60 (5x2)*(1.69)=(3x)1.609
 one year ago

GOODMANBest 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.
 one year ago

sami21Best ResponseYou've already chosen the best response.1
a typo ! correct is (5x2)*(1.94)=(3x)1.609
 one year ago

sami21Best ResponseYou've already chosen the best response.1
ok. u mean this \[\Large \sqrt{3x2}\sqrt{x}=1\] ??
 one year ago

sami21Best ResponseYou've already chosen the best response.1
ok taking square of both sides
 one year ago

sami21Best 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 \[\Large ((3x2)+x2\sqrt{3x2}\sqrt{x})=1\]
 one year ago

GOODMANBest ResponseYou've already chosen the best response.0
Itsokay i will pretend the 2 was really 3
 one year ago

sami21Best ResponseYou've already chosen the best response.1
its ok :) i am notorious for typo mistakes ask anyone here :P
 one year ago

sami21Best 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
 one year ago

GOODMANBest ResponseYou've already chosen the best response.0
Wow, thats good enough! Thank you soo much for your help. I learned a lot!
 one year ago

GOODMANBest ResponseYou've already chosen the best response.0
Also, thank you too @GregTheo
 one year ago

muhammad9t5Best ResponseYou've already chosen the best response.0
\[\sqrt(3x2)\sqrt(x)=1\] add \[\sqrt(x)\] in both sides
 one year ago
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