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December 16th, 2016, 02:46 AM  #11  
Newbie Joined: Dec 2016 From: Canada Posts: 12 Thanks: 0  Quote:
I have one more question to bother you with. This is a question in a worksheet. The equation m log p (n) = q can be written in exponential form as... The answer on the work sheet is p^(q/m)=n but shouldn't it be P^(qm) = n ? According to the power rule? My teacher explained this by writing down for me log p (n) = q / m but I'm confused here. I got my answer from Khans' video here Skip to 4:00 Basically according to the power rule you have Log a (c)^d = bd . He brought the d down to the other side. So in exp form A^(bd) = C^d so shouldn't the answer be p^(mn) = n rather than P^(q/m) = n ? I get the feeling that what Khan is doing is different to what the question is asking. Khan is proving a law whereas as this is manipulating a log equation to exponential form but I'm confused as to how they're different.  
December 16th, 2016, 03:49 AM  #12 
Math Team Joined: Jul 2011 From: Texas Posts: 2,701 Thanks: 1359 
Two ways to do this ... 1. $m\log_p(n)=q$ divide both sides by $m$ ... $\log_p(n)=\dfrac{q}{m}$ change to an exponential ... $n=p^{q/m}$ 2. $m\log_p(n)=q$ rewrite using the power property for logs ... $\log_p(n^m)=q$ change to an exponential ... $n^m=p^q$ Both results are the same. Note ... $n=p^{q/m}$ raise both sides to the $m$ power ... $n^m = \left(p^{q/m}\right)^m = p^{(q/m) \cdot m} = p^q$ 
December 16th, 2016, 04:23 AM  #13 
Newbie Joined: Dec 2016 From: Canada Posts: 12 Thanks: 0 
Okay that makes sense to me but why does Khan in the video do then log a (c)^d = bd . The D is being multiplied rather than divided. Which in exp form is A^(bd) = c^d. Is he talking about something else?

December 16th, 2016, 07:56 AM  #14 
Math Team Joined: Jul 2011 From: Texas Posts: 2,701 Thanks: 1359 
I didn't watch the video ...


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