anonymous
  • anonymous
Log2 x + 5 = 8 - log2 (x + 7)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
add log2 (x + 7) to both sides, substract 5 from both sides, rewrite the log expression log2 x + log2 (x+7)as the log of a product. exponentiate both sides. get x
anonymous
  • anonymous
u should get x = -1 and x = 8, but since x = -1 is outside the domain of the logarithm, reject it
anonymous
  • anonymous
can u show me the workk but i think im doing it completely wrong...heres what i came up with...lol log2 x + log2 (x+7) = 3 log2 [x/(x+7)] 3 [x/(x+7)] = 6 x= 6(x+7)

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anonymous
  • anonymous
ok for step 2, log2 (x(x+7)) = 3, exponentiate both sides using 2, you will get x(x+7) = 8, then by collecting terms, x^2 - 7x - 8 = 0, solve for x
anonymous
  • anonymous
u should get x = 8 and x = -1, but since the log is not defined at x = -1, you must reject this answer
anonymous
  • anonymous
got it?
anonymous
  • anonymous
ohhhh okayy so u get x=8 right??
anonymous
  • anonymous
yup
anonymous
  • anonymous
:)

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