shannondidier 2 years ago Which of the following is the solution of log x + 50.001 = -3 ?

1. shannondidier

here are the answer choices x = 5 x = 7 x = 13 x = 15

2. swissgirl

Well Lets try to isolate x So first we subtract 50.001 from both sides logx=-53.001

3. shannondidier

i typed it wrong, its base x+5 to the 0.001-3

4. swissgirl

Then we know that $$e^{ \log{x}} =x$$ So $$e^{ \log{x}}=e^{-53.001}$$

5. swissgirl

hmmmm Can you retype it please cuz I dont think I am following?

6. whpalmer4

better yet, draw it!

7. vinnv226

@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)

8. shannondidier

|dw:1373413752114:dw|

9. swissgirl

Seems like the base is x+5 not 10

10. whpalmer4

ah, that's much different :-)

11. swissgirl

yaaaaaaaaaaaa

12. whpalmer4

so it is asking us to find a value $$x$$ such that $(x+5)^{-3} = 0.001$

13. whpalmer4

Here's a hint: $x^{-n} = \frac{1}{x^n}$ and $0.001 = \frac{1}{1000}$

14. shannondidier

yeah i understand that. so whats the final answer?

15. 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?

16. whpalmer4

maybe work backwards — what number cubed gives you 1000?

17. shannondidier

x = 5 x = 7 x = 13 x = 15 would it be x=5

18. whpalmer4

it would! $(5+5)^{-3} = 10^{-3} = \frac{1}{10^3} = \frac{1}{1000} = 0.001$

19. shannondidier

thank you!!!

20. whpalmer4

next time, please don't make us do a warm-up problem ;-)