OpenStudy (anonymous):

Pre-Cal :)))

2 years ago
OpenStudy (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 years ago
OpenStudy (phi):

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

2 years ago
OpenStudy (anonymous):

The 1st one lol!

2 years ago
OpenStudy (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

2 years ago
OpenStudy (anonymous):

Ok, then how would u graph it?

2 years ago
OpenStudy (phi):

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

2 years ago
OpenStudy (anonymous):

0.001?

2 years ago
OpenStudy (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 ?

2 years ago
OpenStudy (anonymous):

-3

2 years ago
OpenStudy (phi):

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

2 years ago
OpenStudy (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)

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (phi):

if you have geogebra , you type in the equation

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (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.

2 years ago
OpenStudy (phi):

just type in y= -log(x)

2 years ago
OpenStudy (anonymous):

oH! Hahaha thanks :)

2 years ago
OpenStudy (anonymous):

What about the 2nd part of the question?

2 years ago
OpenStudy (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 ?

2 years ago
OpenStudy (anonymous):

I got (0.316,0.5)

2 years ago
OpenStudy (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 \[ 10^{-y} = t \\ t= 10^{-y} \]

2 years ago
OpenStudy (phi):

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

2 years ago
OpenStudy (anonymous):

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

2 years ago
OpenStudy (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)

2 years ago
OpenStudy (anonymous):

Yes! Thanks so much<3

2 years ago