anonymous
  • anonymous
3. Write down the values of the following without using a calculator. Use your calculator to check your answers for those questions which use base 10. (vii) log_3(square root 27) I don't know what to do with this one, please help!
Mathematics
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anonymous
  • anonymous
3. Write down the values of the following without using a calculator. Use your calculator to check your answers for those questions which use base 10. (vii) log_3(square root 27) I don't know what to do with this one, please help!
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[\log_{3} \sqrt{27}\]
anonymous
  • anonymous
\[\log_{3} \sqrt{27}=\log_{3}\sqrt{3^3}=\log_3(3^3)^{\frac{ 1 }{ 2 }}=\log_3 3^\frac{ 3 }{ 2 }\]
anonymous
  • anonymous
Can you explain why you did that?

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anonymous
  • anonymous
because log and exponentials of the same base are inverses. the \(log_3\) cancels the base of 3 in the exponential. \(log_3 3=1\) \(log_3 3^a=a\) So for your problem \(log_3 3^{\frac{3}{2}}=\frac{3}{2}\)

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