How do you solve #5000(1.09^(12x)) = 9500#?
1 Answer
Jan 7, 2016
Explanation:
Divide both sides by
#1.09^(12x)=1.9#
To get the
#log_1.09(1.09^(12x))=log_1.09 1.9#
#12x=log_1.09 1.9#
Divide both sides by
#x=(log_1.09 1.9)/12#
To find the value of this in a calculator, use the change of base formula, which states that
#log_ab=log_cb/log_ca#
Thus
#log_1.09 1.9=ln1.9/ln1.09#
so
#x=(ln1.9/ln1.09)(1/12)=ln1.9/(12ln1.09)=0.62066899187#