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Which of the following is the solution of log x + 50.001 = -3 ?

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here are the answer choices x = 5 x = 7 x = 13 x = 15
Well Lets try to isolate x So first we subtract 50.001 from both sides logx=-53.001
i typed it wrong, its base x+5 to the 0.001-3

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Then we know that \( e^{ \log{x}} =x\) So \( e^{ \log{x}}=e^{-53.001}\)
hmmmm Can you retype it please cuz I dont think I am following?
better yet, draw it!
@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)
Seems like the base is x+5 not 10
ah, that's much different :-)
so it is asking us to find a value \(x\) such that \[(x+5)^{-3} = 0.001\]
Here's a hint: \[x^{-n} = \frac{1}{x^n}\] and \[0.001 = \frac{1}{1000}\]
yeah i understand that. so whats the final answer?
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?
maybe work backwards — what number cubed gives you 1000?
x = 5 x = 7 x = 13 x = 15 would it be x=5
it would! \[(5+5)^{-3} = 10^{-3} = \frac{1}{10^3} = \frac{1}{1000} = 0.001\]
thank you!!!
next time, please don't make us do a warm-up problem ;-)

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