Melissa_Something
  • Melissa_Something
Log Question:
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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Melissa_Something
  • Melissa_Something
\[\log _{10} 1/\sqrt{10}\]
Melissa_Something
  • Melissa_Something
Sqrt 10/ 10 is wrong :(
Nnesha
  • Nnesha
\[\log_{10} \frac{1}{\sqrt{10}}\] like this ?

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More answers

Jhannybean
  • Jhannybean
Change of base: \(\log_a (x) =\dfrac{\log_b (x)}{\log_b (a)}\)
Melissa_Something
  • Melissa_Something
Oh yes! Lol
Nnesha
  • Nnesha
you can convert square root to an exponent if you want or use change of base formula
jango_IN_DTOWN
  • jango_IN_DTOWN
log(a/b)=log a-log b so the given expression becomes log 1-log sqrt 10 =-log sqrt 10 =-log (10)^1/2=-1/2
Jhannybean
  • Jhannybean
Lets take \(x=\dfrac{1}{\sqrt{10}}\)
Nnesha
  • Nnesha
\[\sqrt{y} \] can be written as \[\rm y^\frac{ 1 }{ 2 }\] so \[\rm \log_{10} \frac{ 1 }{ (10)^\frac{ 1 }{ 2 } }\] move the (10)^/2 at the numerator
Melissa_Something
  • Melissa_Something
So it would be \[\log 1/\sqrt{10} /\log 10\] ??
Melissa_Something
  • Melissa_Something
Oh oh okay
Jhannybean
  • Jhannybean
\[\begin{align} \log_{10} \left(\frac{1}{\sqrt{10}}\right) &=\frac{\log\left(\frac{1}{\sqrt{10}}\right)}{\log(10)}\\& = \frac{\log(1)-\log(\sqrt{10})}{\log(10)} \\&=\frac{-\frac{1}{2}\log(10)}{\log(10)}\\&=-\frac{1}{2} \end{align}\]
Melissa_Something
  • Melissa_Something
Wow thanks for all the support :o
Nnesha
  • Nnesha
typo (10)^{1/2} remember the exponent rule when move base from the numerator to denominator sign of the exponent would change \[\huge\rm \frac{ 1 }{ x^{-m }}= x^m\]
Melissa_Something
  • Melissa_Something
Yes oh my gosh thank you @Nnesha
Nnesha
  • Nnesha
u already got the answer so i'm just gonna work itout \[\log_{10} 10^{-\frac{1}{2}}\] apply the power rule power rule \[\large\rm log_b x^y = y \log_b x\] \[-\frac{1}{2} \log_{10}10\] log_{10} 10 = 1 so left wth -1/2

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