r(x) = 9.7
3ln(1.2)(1.2^x) = 9.7
Note that the answer we'll get is highly dependent on the question being worded correctly. For example, ln(1.2)(1.2^x) is not the same thing as ln( (1.2)(1.2^x) ).
1.2^x = 9.7/(3ln(1.2))
ln(1.2^x) = ln( 9.7/(3ln(1.2)) )
xln(1.2) = ln( 9.7/(3ln(1.2)) )
x = ln( 9.7/(3ln(1.2)) ) / ln(1.2)
x = about 15.772
.
r(x) = 20
x = ln( 20/(3ln(1.2)) ) / ln(1.2)
x = about 19.740