anonymous
  • anonymous
solve for x 3log_(4)x+log_(4)2-log_(4)(x-2) show steps if you can!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Can you please put it in the equation. I can't understand what it says.
anonymous
  • anonymous
*equation?
mathstudent55
  • mathstudent55
\(\Large 3 \log_4 x+ \log_4 2- \log_4 (x-2)\)

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More answers

anonymous
  • anonymous
\[3\log_4x+\log_42-\log_4(x-2)\]
mathstudent55
  • mathstudent55
Is that what you meant? There is no equal sign, so it is not an equation. What do you need to do with it? Write it as a single log? Or is the equal sign missing?
anonymous
  • anonymous
the question just said "Simplify."
anonymous
  • anonymous
I think I just need to write it as a single log since there is no equal sign.
mathstudent55
  • mathstudent55
Ok. I think what that means is to write the entire thing as a single log.
mathstudent55
  • mathstudent55
You need to know these three rules of logs: \(\log a + \log b = \log ab\) \(\log a - \log b = \log \dfrac{a}{b} \) \(\log a^n = n \log a\) The third rule is not needed in this problem, but you need to know it.
anonymous
  • anonymous
yeah, i have those in my notes.
mathstudent55
  • mathstudent55
Look only at the part in red below for now. Use the first rule. How do you combine that sum of logs into one single log? \(\Large \color{red}{3 \log_4 x+ \log_4 2}- \log_4 (x-2)\)
mathstudent55
  • mathstudent55
BTW, I'm sorry, but you do need the third rule. Use the rule of the exponent first on the first log. Then combine the two red logs into one using the first rule.
mathstudent55
  • mathstudent55
Use the third rule (exponent) on the green log below. \(\Large \color{green}{3 \log_4 x} + \log_4 2- \log_4 (x-2)\)
mathstudent55
  • mathstudent55
Can you complete the bottom equation below? |dw:1446502450521:dw|
mathstudent55
  • mathstudent55
|dw:1446502537450:dw|
anonymous
  • anonymous
\[\log_44^3?\]
mathstudent55
  • mathstudent55
|dw:1446503424733:dw|
mathstudent55
  • mathstudent55
\(\large \log_4 x^3\) A number that multiplies the log (such as 3 here) becomes an exponent (an exponent of x here).
mathstudent55
  • mathstudent55
Now that we have the exponent part done, we need to use the first of the 3 rules in the first two logs.
mathstudent55
  • mathstudent55
\(\Large \color{red}{ \log_4 x^3+ \log_4 2}- \log_4 (x-2)\) Now combine the two first logs into the log of a product.

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