Ineed . basically, i need to figure out the dependent and independent value of a function.

here is the situation thing:
the chess club started with a membership of only 4 students, but the membership grew at a rate of 2.56% each week. the number of students is modeled by f(x) = 4(1.0256)x.
i had to make like a question about it. i chose "in how many weeks would there be 12 students? ".
so that made the equation 12 = 4(1.0256)x.
then i had to use logarithms to get to the answer (i got 43.46, if you could fact check this too, that would be lovely.)

so the question is:
let your dependent variable in the function be y. write the function that models the independent variable in terms of y, using logarithms.

i really don't know what it wants me to do,

Step-by-step explanation:

The question is asking you to solve ...

   y = f(x)

for x. (In other words, find the inverse function.)

You already did this using a constant for y. Do the same thing with y instead of the constant.

  y = 4(1.0256^x)

  y/4 = 1.0256^x . . . . . . . divide by 4

  log(y/4) = x·log(1.0256) . . . . . take logs

  log(y/4)/log(1.0256) = x . . . . . divide by the coefficient of x

Now, you have a model for x in terms of y, which is what the question is asking for.

  x = log(y/4)/log(1.0256) . . . . . . . exact expression

When y=12, this is ...

  x = log(12/4)/log(1.0256) ≈ 43.46 . . . . weeks

This is a linear equation in log(y), so can be written as such:

  x = 91.0912·log(y) -54.8424 . . . . . approximate expression

yep

step-by-step explanation: