Question

Which logarithmic graph can be used to approximate the value of y in the equation 3y = 4?

Answer 1

If you have

\[\Large b^x = y\]

then it can be converted to

\[\Large \log_{b}(y) = x\]

Answer 2

Oh wow, it's that simple? Give me one sec

Answer 3

So

\[\Large 3^{y} = 4\]

would turn into

\[\Large y = \log_{3}(4)\]

Answer 4

it seems like x is missing in the original equation \(\Large 3^y = 4\)

Answer 5

Yeah and I'm trying to graph it and I keep getting a straight line

Answer 6

it's a vertical line right?

Answer 7

and hopefully you're typing in "log(4)/log(3)" without quotes

Answer 8

No horizontal and I typed y=log(3,4)

Answer 9

what kind of calculator do you have?

Answer 10

I'm using geogebra

Answer 11

ok do you see the algebra window? It's a subwindow that is usually off to the left.

Answer 12

Yes

Answer 13

there should be an entry that has "line" then underneath that is the equation of the line of the form y = k where k is some fixed number

Answer 14

that value of k is the approximate solution to \[\Large 3^y = 4\]

Answer 15

I don't see that

Answer 16

can you post a screenshot of what you see please?

Answer 17

One sec

Answer 18

ok what you typed in somehow didn't register

Answer 19

this is what you should have gotten

Answer 20

that line 'b' is the line y = 1.26186

Answer 21

Yeah that's the horizontal line I was talking about

Answer 22

odd how it's not showing up in the pic you sent

Answer 23

That's because I deleted it. Sorry

Answer 24

oh that explains it lol, no worries

Answer 25

k :)

Answer 26

anyways, this means that \[\Large y \approx 1.26186\]

Answer 27

K so the new equation is 3^(1.26186)=4?

Answer 28

approximately, yes

now the question is...why do they have these 4 graphs to choose from

Answer 29

it's possible that the x intercept of each graph is the solution to the equation

if this is the case, then we have a problem because 2 graphs share the same x intercept near the x-intercept of 1.26186

Answer 30

so that's why I'm thinking x is missing somewhere

Answer 31

I have no idea what to do

Answer 32

can you take a screenshot of the full problem (ignore the answer choices though, I already see them)

Answer 33

k one more sec

Answer 34

ok

Answer 35

ok so no x, hmm

I think I've eliminated the first and last graphs because they don't cross the x axis near 1.26186

Do you see what I'm referring to?

Answer 36

Yes

Answer 37

However, the middle 2 graphs cross at what appears to be the same x-intercept. In between 0 and 2, so near 1 and possibly near 1.26186.

Answer 38

So if we base it off the x-intercept, then we're stuck between these 2 graphs

Answer 39

Maybe it's b since c would have to be negative right?

Answer 40

Honestly, there's not enough info to pick either one. They both have the same x-intercept (it looks like) which is the point used to approximate the solution for the given equation.

Answer 41

But wouldn't the third have to be negative since it's going downward?

Answer 42

The third graph does have a negative coefficient, but it still has the same x-intercept

Answer 43

all we care about is the x-intercept since we just want to approximate the solution to 3^y = 4

Answer 44

if there was an x in there, then converting it to a logarithmic equation would graph something of the shape of what you see in the 4 choices

that would help find the answer quickly

Answer 45

I'm going to go back into my notes to see if I can figure anything out. Brb

Answer 46

Alright

Answer 47

Absolutely no luck

Answer 48

Does the problem give any hints at all?

Answer 49

None

Answer 50

And I'm guessing you're not able to ask the teacher about this?

This definitely seems like a trick question or something is missing.

Answer 51

Because b or c are both equally likely answer choices

Answer 52

Nope and I think the same thing because it just seems so...incomplete

Answer 53

yeah it seems odd to leave out x

because if x was in there, then you'd have those logarithmic graphs (and not a horizontal line)

Answer 54

Exactly. I'm just gonna try my luck and go with b

Answer 55

I guess that's the only thing you can do

Answer 56

k thanks for your help. I'll give you a medal

Answer 57

you're welcome