we have that
1/16 = 64^x
applying log both sides
log(1/16)=log(64^x)
log 1-log16=x*log64
-log 16=x*log 64
divide by log 64 both sides
x=-log 16/log 64
log 16=log 2^4-----> 4*log 2
log 64=log 2^6-----> 6*log 2
-log 16/log 64=(-4*log 2)/(6*log 2)-----> -4/6------> -2/3
the answer is
x=-2/3