Question

Im so confused pls help

Answer 1

Answer:

  (d)  f(x) = log₆(x)

Step-by-step explanation:

If we use y in place of f(x), we see that ...

  x = 6^y

Taking logs of both sides, we get ...

  log(x) = y·log(6)

  y = log(x)/log(6)

  y = log₆(x) . . . . . . . using the change of base formula

  f(x) = log₆(x)

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Or you can get there more directly using the relation between logs and exponentials:

  $\displaystyle a = b^c\ \leftrightarrow\ c=\log_b(a)$