anonymous
  • anonymous
3 = log8 + 3logx need help please and thankyou
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
start by using \(n\log(x)=\log(x^n)\) to rewrite it as \[3=\log(8)+\log(x^3)\]
anonymous
  • anonymous
then use \(\log(A)+\log(B)=\log(AB)\) to rewrite it as \[3=\log(8x^3)\]
mathslover
  • mathslover
\(\log a + \log b = \log (ab) \) - Next step

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Callisto
  • Callisto
log 8 = log (2^3) = 3 log 2 3 = log8 + 3logx 3 = 3 log 2 + 3 log x 1 = log 2 + log x
mathslover
  • mathslover
here, a = 8 and b = x^3 ...
anonymous
  • anonymous
then rewrite in equivalent exponential form assuming that the log is log base ten, exponential form is \[10^3=8x^3\]
anonymous
  • anonymous
then your puttin 3=x+3
mathslover
  • mathslover
Next step : \(3 = \log (2x)^3 \) \(3 = 3 \log (2x) \) \(1 = log (2x)\)
anonymous
  • anonymous
solve for \(x\) by dividing by \(8\) and then taking the cubed root of both sides
mathslover
  • mathslover
That is : \(1 = \log (2x) \) If base is 10, then 2x = 10 as : \(log_ a a = 1\)
anonymous
  • anonymous
x=5
mathslover
  • mathslover
solve it for x further. \(\bf{2x = 10}\)
anonymous
  • anonymous
\[10^3=8x^3\] \[\frac{10^3}{8}=x^3\] \[\frac{10}{2}=x\]\[5=x\]
mathslover
  • mathslover
Simply use : \(\log _ a a = 1\) , if base is 10, then 2x has to be 10 also. That's it...

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