anonymous
  • anonymous
log8 + log8 (x+2)=1 . Find x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
think you are missing something. i am guessing this is \[log_8(x)+log_8(x+2)=1\]
anonymous
  • anonymous
yes your right
anonymous
  • anonymous
ok in that case straight forward. step one is combine the logs on the right into a single logarithm using \[log(ab)=log(a)+log(b)\] backwards

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anonymous
  • anonymous
you get \[log_8(x)+log_8(x+2)=log_8(x(x+2))\]
anonymous
  • anonymous
so \[log_8(x(x+2))=1\] in equivalent exponential form this mean \[x(x+2)=8^1=8\]
anonymous
  • anonymous
now you have a quadratic equation to solve: \[x(x+2)=8\] \[x^2+2x=8\] \[x^2+2x-8=0\] factor \[(x+4)(x-2)=0\] \[x=-4\] or \[x=2\] but now you have to be careful
anonymous
  • anonymous
because one answer is negative and you cannot take the log of a negative number. so the answer is not -4 or 2, the answer is just 2
anonymous
  • anonymous
Thank you so much :-D <3
anonymous
  • anonymous
welcome hope the steps were clear.

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