shannondidier Group Title Which of the following is the solution of log x + 50.001 = -3 ? one year ago one year ago

1. shannondidier Group Title

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

2. swissgirl Group Title

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

3. shannondidier Group Title

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

4. swissgirl Group Title

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

5. swissgirl Group Title

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

6. whpalmer4 Group Title

better yet, draw it!

7. vinnv226 Group Title

@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 Group Title

|dw:1373413752114:dw|

9. swissgirl Group Title

Seems like the base is x+5 not 10

10. whpalmer4 Group Title

ah, that's much different :-)

11. swissgirl Group Title

yaaaaaaaaaaaa

12. whpalmer4 Group Title

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

13. whpalmer4 Group Title

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

14. shannondidier Group Title

yeah i understand that. so whats the final answer?

15. whpalmer4 Group Title

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 Group Title

maybe work backwards — what number cubed gives you 1000?

17. shannondidier Group Title

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

18. whpalmer4 Group Title

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

19. shannondidier Group Title

thank you!!!

20. whpalmer4 Group Title

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