Question

What logarithmic function represents the data in the table?




x f(x)

25 2
125 3
625 4

Answer 1

Essentially we are trying to figure out what the base of the logarithmic function is since we know it will take the form of:\[\log_{b}x \]

Answer 2

So using that, try to plug in the numbers you are given and see if you can find b, which is the base of the log function.

Answer 3

I honestly don't know how to do this at all... that's why im asking.. I don't get any of it :/ sorry (GO GATORS)

Answer 4

Okay let me help walk you through it. So we know we are looking for a logarithmic function, but we are unsure of the base. So let's start with this as our function:
\[f(x) = \log_{b}x \]

Answer 5

ok

Answer 6

Logarithms have the following property:
\[y = \log_{b}x \approx x = b ^{y}\]

Answer 7

Right?

Answer 8

yes

Answer 9

Okay, so let's try and put in the first entry of the table into our model function.

Answer 10

x = 25, f(x) = 2

Answer 11

\[2 = \log_{b}25 \] correct?

Answer 12

yes so far so good hah

Answer 13

Okay, so now let's do a "log roll" and convert it to the other form that I posted above:
\[25 = b^{2}\]

Answer 14

ok so solve for b?

Answer 15

Yup!

Answer 16

b=5?

Answer 17

Exactly!

Answer 18

hahaha ok good

Answer 19

So now you can plug that in for b in our model equation, and we'll make sure that it works for the other data entries given.

Answer 20

So you should have
\[f(x) = \log_{5}x \]

Answer 21

ok :)

Answer 22

Does that make sense?

Answer 23

Yessir

Answer 24

Thank you!

Answer 25

Great! And we can see that this equation holds true for the other two data entries since
\[3 = \log_{5}125 \]
\[4 = \log_{5}625 \]

Answer 26

Both of those are true, so your equation is:
\[f(x) = \log_{5}x\]

Answer 27

You helped me get a 100 :)

Answer 28

Thanks so much

Answer 29

Fantastic!

Answer 30

No problem!