anonymous one year ago Pre-Cal :)))

1. anonymous

Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.

2. phi

does p(t) = −log10t. mean $p(t)= - \log_{10} t$ or $p(t) = −\log(10t)$?

3. anonymous

The 1st one lol!

4. phi

ok, I just googled it. Yes the first way. $p(t)= - \log_{10} t$ pick some values for t. I would pick powers of 10 (because it is easy to "take the log" ) thus let t= 0.001 (i.e. t= 10^-3 t= 0.01, or t= 10^-2 t= 0.1 or t= 10^-1 t= 1, t= 10^0 t=10 , t= 10^1

5. anonymous

Ok, then how would u graph it?

6. phi

first, what is the log of 10^-3 ? $\log_{10} \left(10^{-3} \right) =$

7. anonymous

0.001?

8. phi

10^-3 is 0.001 the log of 0.001 is the exponent (assuming we use base 10) in other words $\log_{10}(0.001) = \log_{10}\left( 10^{-3}\right)$ what is the exponent ?

9. anonymous

-3

10. phi

ok. $p(t)= - \log_{10} t \\= -1 \cdot \log(0.001) \\= -1 \cdot -3 = 3$

11. phi

so (0.001, 3) is a point on the graph hopefully you can figure out the following points (0.01,2) (0.1, 1) (1,0) (10,-1) (100,-2) (1000,-3)

12. anonymous

yes, I think I can. How could I graph this using technology?

13. phi

if you have geogebra , you type in the equation

14. anonymous

I dont have that/ know what that is lol :)

15. anonymous

I have desmos.com but I wouldnt know how to type that in

16. anonymous

Anyways, I'll figure it out:) No worries!! This is the 2nd part. 2. The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool by 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.

17. phi

just type in y= -log(x)

18. anonymous

oH! Hahaha thanks :)

19. anonymous

What about the 2nd part of the question?

20. phi

zoom in on your graph, and click on the curve when it has y=0.5 what do you get for the x value ?

21. anonymous

I got (0.316,0.5)

22. phi

for ** convert the logarithmic function into an exponential function using y for the pH.*** y= - log(t) or, after multiplying by -1 on both sides: -y = log(t) now make each side the exponent of 10 $10^{-y} = 10^{\log t}$ the right side becomes t $10^{-y} = t \\ t= 10^{-y}$

23. phi

yes, 0.316 is good using the exponential equation $t= 10^{-0.5} = \frac{1}{\sqrt{10}} = 0.316228$

24. anonymous

So, we just converted it right? And that would be the answer to the question?

25. phi

yes, the work to find the exponential form is up above. and I used it to check your answer... and as you see we get the same number (rounded of course)

26. anonymous

Yes! Thanks so much<3