by Guest » Fri Oct 23, 2015 7:31 pm
-3.2^(x+7)+3.2^(x+9)=36
OR another approach would be........
keep it as simple as possible first divide across by 3
-2^(x+7) + 2^(x+9)=12 ...then re-arrange
2^(x+9) = 12 + 2^(x+7) ...then divide across by 2^(x+9)
1 = [12 / 2^(x+9)] + [2^(x+7) / 2^(x+9)]
1 = [12 / 2^(x+9)] + [2^(x+7-x-9)] ...subtract indices
1 = [12 / 2^(x+9)] + [2^(-2)] .....2 to power -2 is a quarter
1 = [12 / 2^(x+9)] + [1/4] .....subtract the 1/4 both sides
3/4 = [12 / 2^(x+9)] ....multiply by 4 across
3 = [48 / 2^(x+9)] ...... divide by 3 across
1 = [16 / 2^(x+9) ...cross multiply
2^(x+9) = 16 = 2^4
therefore equating indices .... X + 9 = 4 OR X = -5