anonymous
  • anonymous
Solve 2 log 2x = 4. Round to the nearest thousandth if necessary. How do I solve this?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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Yttrium
  • Yttrium
Convert this first into exponential function. Do you know how to do that?
anonymous
  • anonymous
No, I don't.
DebbieG
  • DebbieG
is it: \[\Large 2\log_{2}x=4\] or \[\Large 2\log (2x)=4\] ??

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anonymous
  • anonymous
\[2\log (2x)=4 \]
Yttrium
  • Yttrium
Always take note that \[\log_{a} b = c\] is also equal to \[a ^{c} = \] So the convertion of it to exponential will be \[10^{4} = 2x ^{2}\] Just tell me if you don't get it.
anonymous
  • anonymous
I don't understand. The possible answers are: A) 50 B) 0.5 C) \[50\sqrt{2}\] D) 2
DebbieG
  • DebbieG
There are a couple of ways to start this, but first off, you need to have an "isolated" log expression on the LHS, that is, not a coefficient of 2 in front of that log function. since the right hand side is just a number, that's easy enough to deal with here by dividing both sides by 2: \(\Large \dfrac{2\log(2x)}{2}=\dfrac{4}{2}\) so: \(\Large \log(2x)=2\) Now, at this point it's really just a matter of understanding what the log function MEANS: \(\Large \log_{b}x=y\) means exactly that \(\Large b^y=x\) In other words, \(\Large \log_{b}x=y\) MEANS THAT y is the POWER to which you take the base 2, to get x. So the exponential form and the log form are just two sides of the same coin: the output of the log is the exponent of the exponential; and the input of the log is the output (the result) of the exponential. And, you also need to know that the notation: \(\Large \log a\) (with no "base" stated) means that you have a base of 10. In other words, \(\Large \log x=\log_{10}x\) So can you use that to figure out what x is, in \(\Large \log(2x)=2\) ? You should first convert it to the exponential form, simplify what you can, and you should have a simple little equation to solve for x. :)

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