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January 10th, 2017, 06:38 PM  #1 
Newbie Joined: Jan 2017 From: Canada Posts: 2 Thanks: 1  Applying laws of logarithms and relations
Hey, I'm stumped on the second part of a question that asks: Here's my simplification: I'm unsure if I took it too far, however I don't understand the second part of the question. How would they be related? Any and all help would be great, thanks. 
January 10th, 2017, 06:54 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,593 Thanks: 937 Math Focus: Elementary mathematics and beyond 
$$\begin{align*}y&=\frac14\log_2\left[(8x56)^{16}\right]12 \\ &=16\cdot\frac14\log_2(8x56)12 \\ &=4\log_2(8x56)12 \\ &=4\log_2[8(x7)]12 \\ &=4\left(\log_28+\log_2(x7)\right)12 \\ &=4(3+\log_2(x7))12 \\ &=12+4\log_2(x7)12 \\ &=4\log_2(x7)\end{align*}$$ Perhaps they are asking for you to state that each representation of $y$ has domain $x > 7$. 
January 10th, 2017, 07:01 PM  #3 
Newbie Joined: Jan 2017 From: Canada Posts: 2 Thanks: 1 
I see. Thank you for the correction as well, Greg


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