Hello!

Question

Could someone please take a look at the problem below and let me know if I made mistakes in simplifying the given equation? I'm quite certain that I did make a mistake somewhere because the original equation and its simplified form give different graphs when plotted. I would greatly appreciate any help!

y=1/4log2(8x-56)^16 -12
y=(16)(1/4)log2(8x-56)-12
y=4log2(8x-56)-12
y=4log2(8x) : 4log2(56) -12
y=log2(8x)^4 : 4log2(56) -12
y=log2((8^4)(x^4)) : 4log2(56) -12
y=log2(8^4) + log2(x^4) : 4log2(56) -12
y=log2(2^12) + log2(x^4) : 4log2(56) -12
y=12 + log2(x^4) : 4log2(56) -12
y=log2(x^4) : 4log2(56)
y=4log2(x) : 4log2(56)
y=4log2(x-56)

Answer 1

Your major mistake is in line 4
You are basically saying
log(A-B) = logA/logB
there is no such relation!

From line 3:
y=4log₂(8x-56)-12
= 4log₂(8(x-7)) - 12
= 4log₂8 + 4log₂(x-7) - 12
= 4(3) + 4log₂(x-7) - 12
= 4log₂(x-7) , where x>7

Answer 2

Yes you are right, there is no such relation. Thank you so much for your help!