anonymous
  • anonymous
Exponential Equations help? Determine the exact value of x: (1/8)^(x-3) = 2 * 16^(2x+1)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Are you using logarithms to solve?
anonymous
  • anonymous
can it be solved without logarithms??
anonymous
  • anonymous
I don't know how to solve w/o logs

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anonymous
  • anonymous
okay...logarithms are fine then :)
anonymous
  • anonymous
Haha :) First, take the log of both sides
anonymous
  • anonymous
Then apply your log rules...in other words......
anonymous
  • anonymous
\[\log (1/8)^{x-3}= (x-3) \log (1/8)\]
anonymous
  • anonymous
and \[\log (2 * 16^{2x +1}) = \log 2 + \log 16^{2x+1}\]
anonymous
  • anonymous
this equals \[\log 2 + (2x+1) \log 16\]
anonymous
  • anonymous
so now you have\[(x-3) \log (1/8)= \log 2 + (2x + 1) \log 16\]
anonymous
  • anonymous
evaluate the logs and solve the equation for x
anonymous
  • anonymous
There may be another way to solve, but I'm not sure
anonymous
  • anonymous
thanks :) ..but can you explain what you mean by evaluate the logs? i've never done them before, really. :S
anonymous
  • anonymous
ok, forget all that....i just figured out a better way :)
anonymous
  • anonymous
lol okay
anonymous
  • anonymous
1/8 = \[2^{-3}\]
anonymous
  • anonymous
and 16 = \[2^{4}\]
anonymous
  • anonymous
This gives you \[2^{-3(x-3)}= 2^{1}*2^{4(2x+1)}\]
anonymous
  • anonymous
For the exponents, use distributive property
anonymous
  • anonymous
\[2^{-3x+9}= 2^{1}*2^{8x +1}\]
anonymous
  • anonymous
on the right side, you can combine those by adding expontents
anonymous
  • anonymous
\[2^{-3x+9}=2^{8x+2}\]
anonymous
  • anonymous
Now, since the bases are equal, this means the exonents are =, so\[-3x + 9 = 8x + 2\]
anonymous
  • anonymous
Then, solve the equation for x
anonymous
  • anonymous
haha....that was easier than logs :)
anonymous
  • anonymous
yay! this makes so much sense to me. thanks so much :)
anonymous
  • anonymous
You're very welcome!

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