anonymous
  • anonymous
Use properties of logs to simplify the expression
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\log_{9}(x-\sqrt{x ^{2}-45})+ \log_{9}(x+\sqrt{x ^{2}-45})\]
anonymous
  • anonymous
so what I got was \[\log_{9}45 \] but that's not one of my answer choices. what am I doing wrong?
anonymous
  • anonymous
these are the answer choices: 1. 1 + log9 5 2. log5 9 3. 1 + log5 9 4. log9 5 5. 9 + log9 5

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More answers

mathstudent55
  • mathstudent55
The sum of logs is the log of the product. \( \log_x a + \log_b y = \log_b xy \)
mathstudent55
  • mathstudent55
\(\log_{9}(x-\sqrt{x ^{2}-45})+ \log_{9}(x+\sqrt{x ^{2}-45}) \) \( = \log_{9}[(x-\sqrt{x ^{2}-45})(x+\sqrt{x ^{2}-45})] \) Now use "the product of a sum and a difference equals the difference of two squares" pattern to simplify.
anonymous
  • anonymous
45?
mathstudent55
  • mathstudent55
\( = \log_9 45\) You are correct, but you can go furhter because 45 = 9 * 5.
anonymous
  • anonymous
oh ok. I just need to know how to do the next step.
mathstudent55
  • mathstudent55
\( = \log_9 (9 \times 5) \) Use the rule: log of product = sum of logs.
mathstudent55
  • mathstudent55
\( = \log_9 9 + \log_9 5 \) \(\log_9 9\) can be simplified since \( \log_b b = 1\)
anonymous
  • anonymous
so \[1+\log_{9}5 \]
mathstudent55
  • mathstudent55
Exactly. Good job!

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