## anonymous one year ago Convert the logarithmic function into an exponential function using y for the pH. p(t) = −log10t. I really need help with this, any help is appreciated

1. SolomonZelman

In general: A = -log$$\large \rm _{_B}$$(C) A = log$$\large \rm _{_B}$$(C$$^{-1}$$) A = log$$\large \rm _{_B}$$(1/C) 1/C = B$$\Large ^{\rm _{^A}}$$

2. SolomonZelman

or, alternatively, you can say, A = -log$$\large \rm _{_B}$$(C) -A = log$$\large \rm _{_B}$$(C) C = B$$\Large ^{\rm _{^{{\bf \LARGE-}A}}}$$

3. anonymous

This is simple. I also did this for FLVS. So now you will have the equation. y= −log (t) because $\log_{10}$ is the same as log. Now remember this? $b^y = x$ and $y = \log_{b} x$

4. anonymous

@fashionismybesty are you still there?

5. anonymous

Yes I do remember this (I'm also on flvs) and I'm just confused because logarithms usually equal x and now it equals y

6. anonymous

@whatdoesthismean

7. anonymous

Where did you hear logarithms equal x? it could equal a,b,c,d,e,f,d,h, and etc. Logarithms like log (1) would equal 1, and so on.

8. anonymous

And NO log (2) is not 2. Log 2 would be 0.3010299957....

9. anonymous

So anyway let us solve this problem.

10. anonymous

Ok

11. anonymous

$x = b^y$ Is a exponential function. We have $y = -\log (t)$ Remember that $\log_{x} (y)^z = z \log_{x} (y)$

12. anonymous

yes, which means that log(t^-1)=y

13. anonymous

So in this case then $y=−\log(t)$ would become $y = \log (t)^-1$

14. anonymous

So then using $b^y = x$ and $y = \log_{b} x$ We get, $10^y = t^-1$

15. anonymous

i mean $t ^{-1}$

16. anonymous

now remember, $t^{-1} = \frac{ 1 }{ t }$

17. anonymous

But when you graph the exponential function, isn't it supposed to be a reflection of the logarithm over the y-axis? It isn't when I graph $10^y=t^-1$

18. anonymous

t^-1=10^y I mean

19. anonymous

But we're not done. $t^{-1} = 10^y$ and $\frac{ 1 }{ t } = 10^y$ just don't work. But wait, we have a way. remember, $t^{-1} = 10^y$ is equivalent to $t = 10^{-y}$

20. anonymous

Sorry about taking a long time, my computer is glitching when i use equation

21. anonymous

It's fine and thanks for the help so much! for the y to become negative, you just multiply it by the -1 exponent right?

22. anonymous

yeah

23. anonymous

I'm still a little bit confused because the graph of the exponential functions is supposed to be the reflection over the y axis of the logarithm and it isn't

24. anonymous

That is because this is the exponential function FORM of the logarithmic function p(t). Exponential functions are the inverse of the logarithmic function, so the exponential function of p(t) would be y = 10^x. THAT would be the reflection over the y - axis of p(t). In this question we need to just find the FORM of p(t), not the exponential function (or inverse)

25. anonymous

Oh, that makes a lot of sense. Thanks again!