Solve: log 5 (c^x) = d

I am trying this question but I am not sure I am on the right track.
log base 5 (c^x) = d

I am thinking we should take an exponential function for both sides in the form of a^x so,
log base a (a^x)=x
So, do we take a^cx for both sides? then c^x= a^cx.d; cx/d= a^cx; cx= ln (cx/d); cx= ln cx-ln d
but then again, I don't see where you can go from here

use the log rule: log (a^b) = b log (a).

So you get: x log5(c) = d

From here it's fairly easy to transpose to whatever variable you're interested in.
x = d/log(c)
d = xlog(c)

log 5 (c) = d/x
c = 5^(d/x)