shannondidier
Which of the following is the solution of log x + 50.001 = -3 ?
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shannondidier
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here are the answer choices x = 5
x = 7
x = 13
x = 15
swissgirl
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Well Lets try to isolate x
So first we subtract 50.001 from both sides
logx=-53.001
shannondidier
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i typed it wrong, its base x+5 to the 0.001-3
swissgirl
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Then we know that \( e^{ \log{x}} =x\)
So \( e^{ \log{x}}=e^{-53.001}\)
swissgirl
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hmmmm
Can you retype it please cuz I dont think I am following?
whpalmer4
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better yet, draw it!
vinnv226
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@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)
shannondidier
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|dw:1373413752114:dw|
swissgirl
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Seems like the base is x+5 not 10
whpalmer4
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ah, that's much different :-)
swissgirl
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yaaaaaaaaaaaa
whpalmer4
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so it is asking us to find a value \(x\) such that \[(x+5)^{-3} = 0.001\]
whpalmer4
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Here's a hint: \[x^{-n} = \frac{1}{x^n}\] and \[0.001 = \frac{1}{1000}\]
shannondidier
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yeah i understand that. so whats the final answer?
whpalmer4
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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
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maybe work backwards — what number cubed gives you 1000?
shannondidier
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x = 5
x = 7
x = 13
x = 15
would it be x=5
whpalmer4
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it would!
\[(5+5)^{-3} = 10^{-3} = \frac{1}{10^3} = \frac{1}{1000} = 0.001\]
shannondidier
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thank you!!!
whpalmer4
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next time, please don't make us do a warm-up problem ;-)