solve and express in terms of natural logs: 2^2x + 2^x - 90 = 0

Question

This is a an exponential equation that needs to be solved in terms of natural logs

Answer 1

Let y=2^x then y^2+y-90=0=(y+10)(y-9), so y=2^x=-10 or 9. Since 2^x cannot be negative, 2^x=9, xlog(2)=log(9), and x=log(9)/log(2)=3.17 approx. The logs can be to any base.