anonymous
  • anonymous
Which of the following is the solution of log x + 50.001 = -3 ?
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
here are the answer choices x = 5 x = 7 x = 13 x = 15
swissgirl
  • swissgirl
Well Lets try to isolate x So first we subtract 50.001 from both sides logx=-53.001
anonymous
  • anonymous
i typed it wrong, its base x+5 to the 0.001-3

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swissgirl
  • swissgirl
Then we know that \( e^{ \log{x}} =x\) So \( e^{ \log{x}}=e^{-53.001}\)
swissgirl
  • swissgirl
hmmmm Can you retype it please cuz I dont think I am following?
whpalmer4
  • whpalmer4
better yet, draw it!
anonymous
  • anonymous
@shannondidier What should we use as the base of the unspecified "log?" Some people interpret this as log base 10, others interpret it as the natural log (base e)
anonymous
  • anonymous
|dw:1373413752114:dw|
swissgirl
  • swissgirl
Seems like the base is x+5 not 10
whpalmer4
  • whpalmer4
ah, that's much different :-)
swissgirl
  • swissgirl
yaaaaaaaaaaaa
whpalmer4
  • whpalmer4
so it is asking us to find a value \(x\) such that \[(x+5)^{-3} = 0.001\]
whpalmer4
  • whpalmer4
Here's a hint: \[x^{-n} = \frac{1}{x^n}\] and \[0.001 = \frac{1}{1000}\]
anonymous
  • anonymous
yeah i understand that. so whats the final answer?
whpalmer4
  • whpalmer4
okay, look at your answer choices. do any of them + 5 = a number that when raised to the -3 power = 0.001, or when raised to the 3 power = 1000?
whpalmer4
  • whpalmer4
maybe work backwards — what number cubed gives you 1000?
anonymous
  • anonymous
x = 5 x = 7 x = 13 x = 15 would it be x=5
whpalmer4
  • whpalmer4
it would! \[(5+5)^{-3} = 10^{-3} = \frac{1}{10^3} = \frac{1}{1000} = 0.001\]
anonymous
  • anonymous
thank you!!!
whpalmer4
  • whpalmer4
next time, please don't make us do a warm-up problem ;-)

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