aem9296
  • aem9296
Simplify (see more below)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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aem9296
  • aem9296
|dw:1377981407623:dw|
zepdrix
  • zepdrix
\[\Large \log_6\left(\frac{36}{6^{-10}}\right)\] The first thing we should do is ~ Write our numerator with a base of 6. How can we rewrite 36? :o hmmm \[\Large 36=6^?\]
zepdrix
  • zepdrix
Comeon lexi! :D this is an easy step! heh

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aem9296
  • aem9296
hahah i know its 6^2 but what do you have to do with that? haha
zepdrix
  • zepdrix
\[\Large \log_6\left(\frac{6^2}{6^{-10}}\right)\] Ok ok good. Our next step is to divide the exponentials. Remember the rule for dividing exponentials?\[\Large \frac{x^a}{x^b} \quad=\quad x^{a-b}\] When dividing terms of similar bases, we `subtract` the exponents.
zepdrix
  • zepdrix
So what does that leave you with when you divie those exponentials? :O
aem9296
  • aem9296
so wait like 2-(-10)?
zepdrix
  • zepdrix
yes good good.
aem9296
  • aem9296
wouldnt that be 12?
zepdrix
  • zepdrix
6^12 ya :)
aem9296
  • aem9296
yayyy hahah thanks!!
aem9296
  • aem9296
one more question. when it leaves you with log6(6^12) what would it be? on my sheet which is multiple choice it gives me some numbers. how do i do it further?
zepdrix
  • zepdrix
Ah sorry bout that, had to take a phone call.
zepdrix
  • zepdrix
So you got it to this point? \[\Large \log_6\left(6^{12}\right)\] From here we would apply a rule of logarithms:\[\Large \color{royalblue}{\log(a^b) \quad=\quad b\cdot \log(a)}\]
zepdrix
  • zepdrix
Understand how that will allow us to move the 12 outside? :o
aem9296
  • aem9296
Oh yea okay so then the log6(6)=1 so the answer would be 12x1 which is 12?
zepdrix
  • zepdrix
yay good job \c:/

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