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a) 2ˣ = 1/8
2ˣ = 1/2³ = 2⁻3
2ˣ = 2⁻³ bases iguales (2) y los exponentes son iguales por tanto x =-3
b) 2ˣ⁺¹ +2ˣ +2ˣ⁻¹ = 14 descomponiendo
2ˣ.2¹ +2ˣ + 2ˣ.2⁻¹ = 14 factor común 2ˣ
2ˣ{2+1+1/2} = 14
2ˣ{ (4+2+1)/2 = 14
2ˣ[ 7/2] = 14
2ˣ.7 = 14*2
2ˣ.7 = 28
2ˣ =28/7
2ˣ = 4
2ˣ = 2² entonces x = 2
c) 6²ˣ = 1296 descomponemos 1296 nos da 6⁴
6²ˣ = 6⁴ recuerda bases iguales exponentes iguales
2x = 4
x =4/2
x =2
d) 2ˣ⁻¹ = 8 descomponiendo
2ˣ.2 = 8
2ˣ = 8/2
2ˣ = 4
2ˣ = 2²
x= 2
e) 3ˣ.9ˣ = 9³ descomponemos en una sola base 3
3ˣ .(3²)ˣ = (3²)³
3ˣ.3²ˣ = 3⁶
3ˣ ⁺²ˣ = 3⁶
3³ˣ =3⁶
3x = 6
x =6/3
x =2
f) 2⁵⁻²ˣ=1/16 descomponiendo y recuerda 1/16 = 16⁻¹ = 2⁻⁴
2⁵.2⁻²ₓ = 2⁻⁴
2⁻²ˣ = 2⁻⁴/2⁵ subiendo al numerador 2⁵ se cambia de signo
2⁻²ˣ = 2⁻⁴.2⁻⁵
2⁻²ˣ =2⁻⁹
-2x = -9
x= -9/-2
x= 9/2 los siguientes son semejantes al enciso b