Find the value of c so that f '(c) = ln16 for f(x) = 2^x.?

f'(x) = (2^x)(ln(2))

f'(c) = (2^c)(ln(2)) = ln(16)

2^c = ln(16) / ln(2)

2^c = 4

c = log (base 2) of 4

c = 2

f(x) = 2^x = e^(x ln 2)

f'(x) = ln 2 e^(x ln 2)

= ln 2 2^x

ln 2 2^c = ln 16

=> 2^c = 4

=> c = 2