anonymous
  • anonymous
Question in comments, can someone help? :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[4*\log_{x}2=\log_{2}x+3 \] (4*logx 2 = log2 x + 3)
anonymous
  • anonymous
what is your question, exactly?
anonymous
  • anonymous
Find x ? :D

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anonymous
  • anonymous
i think you can start by putting logx 2=log2 2/ log2 x
anonymous
  • anonymous
The hint we get is change the base... There's formula \[\log_{a} b=\frac{ \log_{c}b }{ \log_{c}a }\] But I tried, I can't solve it
anonymous
  • anonymous
you got then 4log2 2=(log2 x)*(log2 x + 3) and finally: (log2 x)^2+3log2 x + 4log2 2=0 now i think you can substitute log2 x by u, solve the quadratic equation and then once you have the values of u, compute the values for x: log2 x=u -----> x=2^u
anonymous
  • anonymous
i didn't get the answer, but i think the procedure is correct
anonymous
  • anonymous
Oh, I think I get the idea, I'll try to solve it now, thank you! That was exactly what I was doing but I didn't saw that I can change log2 x with u and get quadratic
anonymous
  • anonymous
first write log 2 x into 1/(logx 2) then t=logx 2 solve it!
anonymous
  • anonymous
hint:you will get two values that just one of them is acceptable
anonymous
  • anonymous
I got for x 2 and 1/16, why is only one acceptable?
anonymous
  • anonymous
i think both are acceptable
anonymous
  • anonymous
So and I, thanks guys, you helped me a lot :) It was important to me to get the idea how to do it, cause exam is tomorrow, and that was the only one I was struggling :) Thank you, all the best!

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