anonymous
  • anonymous
solve for x? 6^-x-2=13^-8x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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experimentX
  • experimentX
take log on both sides,
anonymous
  • anonymous
$6^{-x-2}=13^{-8x}$ ?
anonymous
  • anonymous
yes

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anonymous
  • anonymous
\[6^{-x-2}=13^{-8x}\]
anonymous
  • anonymous
right
anonymous
  • anonymous
\[\log_{10}{6^{-x-2}}= \log_{10}{13^{-8x\ [\rightarrow x = (-2\log_{10}{6} )/(\log_{10}{6}-8\log_{10}{} )\]}}\]
anonymous
  • anonymous
\[6^{-x-2}=13^{-8x}\implies (x+2)\ln(6)=8xln(13)\implies 8x \ln(13)-x \ln(6)=2 \ln(6)\]\[=x(8 \ln(13)- \ln(6))=2 \ln(6)\implies x=\frac{2 \ln(6)}{8 \ln(13)- \ln(6)}\]
anonymous
  • anonymous
the same log 10 or log e
anonymous
  • anonymous
Pretty cool, no?
anonymous
  • anonymous
ok, cool
anonymous
  • anonymous
Yours was perfectly correct, but I thought maybe somebody would benefit from a little more detail.
anonymous
  • anonymous
yea, i expalin no detail

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