Question

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

Answer 1

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\(\Large ^{\rm _{^A}}\)

Answer 2

or, alternatively, you can say,

A = -log\(\large \rm _{_B}\)(C)

-A = log\(\large \rm _{_B}\)(C)

C = B\(\Large ^{\rm _{^{{\bf \LARGE-}A}}}\)

Answer 3

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

\[y = \log_{b} x\]

Answer 4

@fashionismybesty are you still there?

Answer 5

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

Answer 6

@whatdoesthismean

Answer 7

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.

Answer 8

And NO log (2) is not 2.

Log 2 would be 0.3010299957....

Answer 9

So anyway let us solve this problem.

Answer 10

Ok

Answer 11

\[x = b^y\]
Is a exponential function.

We have
\[y = -\log (t)\]

Remember that

\[\log_{x} (y)^z = z \log_{x} (y)\]

Answer 12

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

Answer 13

So in this case then

\[y=−\log(t)\]

would become

\[y = \log (t)^-1\]

Answer 14

So then using

\[b^y = x\]

and

\[y = \log_{b} x\]

We get,

\[10^y = t^-1\]

Answer 15

i mean

\[t ^{-1}\]

Answer 16

now remember,

\[t^{-1} = \frac{ 1 }{ t }\]

Answer 17

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 \[10^y=t^-1\]

Answer 18

t^-1=10^y I mean

Answer 19

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
\[t = 10^{-y}\]

Answer 20

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

Answer 21

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?

Answer 22

yeah

Answer 23

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

Answer 24

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)

Answer 25

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