Question

Algebra 2 logarithms help!!!!!

Answer 1

@phi pls help!!

Answer 2

What do you not understand? We aren't just going to do the whole homework for you. What aren't you understanding?

Answer 3

I'm confused on what to do for #2. I dont know where to start. Here's my answer for #1

Answer 4

@adam.bloedel

Answer 5

For #1, they ask where the pH is 0 (at t=0)
and where the pH is 1
you did not answer this part. the formula they used is pH= -log_10(t)
you want to find t when -log(t) = 1 ---> log(t)= -1 --> t = 1/10

Answer 6

Isn't it at 0.5? @phi Or do you mean it's 1/10? Sorry, this has been the most confusing chapter of algebra 2 for me.

Answer 7

Let me see if I can make it clearer.
First, we start with their definition (I'll use x instead of t)
pH= -log(x)
Here is a graph between x=0 and about 1.

Answer 8

@phi and p is the y axis right?

Answer 9

Do you get that "logs" are really exponents ?
(we will stick with base 10)

10 i.e. 10^1 has log (10) = 1
100 has log(100)= 2 (because 100= 10^2)

now if we go smaller
0.1 (which is 1/10 or 10^-1) log(0.1)= -1
0.01 log(0.01)= -2
0.0000000001 (very close to zero) has log= very negative number

the plot would look like this

Answer 10

yes, the y axis is pH

so far I plotted the pH graph (which is -log(x) )
and after that the "normal" log graph y= log(x)
putting in the minus sign "flipped" the normal log graph to look like the pH graph

Answer 11

I'm not gonna lie, I still really don't know what a logarithm is. And so when the pH value is 0 is when the other value is 1, right?

Answer 12

yes, "log" is a very lousy name. Makes as much sense as calling them turnips.

but log is *exponent*

so some logs you know:

For *base 10*
what exponent is on the 10 to "make a 10"? 10^1
the exponent of 10 is 1
the exponent of 100 is 2 (first write 100 as 10^2, then look at the exponent)

what is the exponent on 10 (call it x) so that 10^x = 1
0 because 10^0 = 1
the log of 1 is 0

Answer 13

does log always equal 10?

Answer 14

you mean do we always use a base equal to 10
lots of times. when learning about logs they teach about using different bases, but we usually only use base 10 or base e (in which case we type ln rather than log)

Answer 15

The thing is, I don't understand what I'm trying to find.

Answer 16

log(A) means
what is the exponent, x, of 10 to that 10^x = A

Answer 17

By the way.. @sierraurb
\(\Huge\bf \color{yellow}{Welcome~to~OpenStudy!!}\hspace{-310pt}\color{cyan}{Welcome~to~OpenStudy!!}\hspace{-307.1pt}\color{midnightblue}{Welcome~to~\color{purple}{Open}}\color{blue}{Study!!!!}\)

Answer 18

Okay, that makes more sense!

Answer 19

so for 10^-y=0.50 i need to find what exponent on 10 makes it equal to 0.50?

Answer 20

The only method I can think of solving that by is guess and check.

Answer 21

meanwhile, can you figure out what x value gives a pH= 1?

in other words
-log(x) = 1
what is x ?

first, multiply both sides by -1 to get
log(x) = -1

log(x) =-1
means if the exponent of 10 is -1, we get x
\[ x = 10^{-1} \]

Answer 22

or x = 1/10

if you look at the graph, and zoom in, you see that the curve is 1 about halfway between x=0 and x=0.2

Answer 23

Here it is, zoomed in

Answer 24

I don't understand how you came to "log(x) =-1
means if the exponent of 10 is -1, we get x"

Answer 25

log(x) is a way to say
the exponent of 10

log(x)= -1
means the exponent of 10 is -1

the "x" is what 10 to that exponent equals.

Answer 26

example

log(0.1) = -1
means
exponent of 10 is -1
10^-1 = 0.1

Answer 27

That makes soooo much sense!!!!!! Thank you!!! So for ex. log(y)=z the exponent of 10 is z, and 10^z=y

Answer 28

yes

Answer 29

Now i need to use this info on #2..

Answer 30

it still takes time to get used to these ideas... even now I have to think about it.

Answer 31

So the exponent of 10 is 0.5?

Answer 32

And 10^0.5=-y?

Answer 33

So y is about -3.1?

Answer 34

oops, I did that backwards.

they say "raise the ions" by 0.5 which means the x axis
the pH= -log(0.5) (we want the exponent that gives 0.5)

Answer 35

we can look on the graph a see what exponent "goes with" the x=0.5

Answer 36

That's about 0.3 by looking on the graph right

Answer 37

yes

Answer 38

But what about the 3.1 i got earlier?

Answer 39

the earlier 3.1 we did it backwards... we did 10^0.5 = 3.1
what we want is 10^-0.3 = 0.5 (remember we are plotting -log(x) )

Answer 40

Oh we wanted to find what exponent on 10 made it equal 0.5? And that exponent is 0.3 right?

Answer 41

yes, exactly (though because we are doing -log(x), if you check with a calculator, you will find 10^0.3 = 2 and 10^-.3 = ½ )
in other words, 10^0.3 is not 0.5, but our graph is really 10^-x
and when we read off 0.3 (which is the correct answer) it represents 10^-0.3 )

if that is totally confusing forget about it!

btw, if you have time, watch
http://www.khanacademy.org/math/algebra2/logarithms-tutorial

Answer 42

Thank you so so so much for helping me!! I can't explain how much I appreciate it :)

Answer 43

so to finish #2
you plotted
y = -log(x)
which is the same as
-y = log(x)
10^(-y) = x
if we go to x=0.5 we can read off -y = 0.3

Answer 44

for #3


here is a graph of the variations