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Math·Advanced Math·Equivalent expressions

hard

For the function $f$, for each increase in the value of $x$ by $c$, where $c$ is a positive constant, the value of $f(x)$ increases by a factor of 27. Which of the following equivalent forms of the function $f$ displays $1/c$ as a coefficient of $x$?

A

$f(x)=32(3{)}^{\frac{1}{2}x}$

B

$f(x)=32(27{)}^{\frac{1}{c}x}$

C

$f(x)=32(9{)}^{\frac{1}{4}x}$

D

$f(x)=32{\left(27^{\frac{1}{3}x}\right)}^{\frac{1}{2}}$