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January 10th, 2017, 06:38 PM   #1
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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.
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January 10th, 2017, 06:54 PM   #2
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$$\begin{align*}y&=\frac14\log_2\left[(8x-56)^{16}\right]-12 \\
&=16\cdot\frac14\log_2(8x-56)-12 \\
&=4\log_2(8x-56)-12 \\
&=4\log_2[8(x-7)]-12 \\
&=4\left(\log_28+\log_2(x-7)\right)-12 \\
&=4(3+\log_2(x-7))-12 \\
&=12+4\log_2(x-7)-12 \\
&=4\log_2(x-7)\end{align*}$$

Perhaps they are asking for you to state that each representation of $y$ has domain $x > 7$.
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January 10th, 2017, 07:01 PM   #3
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I see. Thank you for the correction as well, Greg
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