Ecuaciones Exponenciales

  • November 2019
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4to. 1ra. T. T. - Matemática Prof. Flavia Terrizzano

Ecuaciones exponenciales Ejemplos •



3 x+2 = 729 3x+2 = 36 x+2=6 x=6–2 x=4

(8 )

x 2

1 64 1 = 6 2

: 29 x =

82 x : 29 x

(2 )

al tener la misma base, puedo igualar los exponentes.

3 2x

: 2 9 x = 2 −6 2 6 x : 2 9 x = 2 −6 2 6 x −9 x = 2 −6 2 −3 x = 2 −6 -3x = -6 x = (-6) : (-3) x= 2 Ejercitación 1) Resolver las siguientes ecuaciones exponenciales 5 x + 1 = 625 Rta. x = 3 x x+1 2.3 + 3 = 45 Rta. x = 2 5. 2 x + 2 x + 3 =208 Rta. x = 4 x x–2 3.5 +5 = 380 Rta. x = 3 7 e) 2 x + = 2 x + 3 Rta. x = 4 -2 27 = 81 f) Rta. x = 3x -1 3 x +1  2 g)  −  Rta. x = =1  3 1 − 3 2 h) 2 x −1 = 256 Rta. x = 3 4 3 x −2 i) Rta. x= = 128 2x 11 5 j) 2 . 3 x – 1 + 3 x + 1 = 297 Rta. x = 4 4.3x–4=0 Rta. x = 0 x x 2 . 2 – 10 . 2 + 4 = 0 Rta. x = -1 3 x + 1 + 3 x – 1 = 90 Rta. x =3 3x+9x Rta. x =2 1 2 27 x +1 = 9 5 x Rta. x = 3 ó x = 3 a) b) c) d)

k) l) m) n) o)

2

p) 7 2 x − 3 x − 2 = 1 Rta. x = 2 ó x = 1 − 2 x q) 2 + 4 x = 72 Rta. x = 3 r) 2 2x + 2 x – 2 = 0 Rta. x =0 s) 3 x – 12 + 27 . 3 –x = 0 Rta. x = 2 ó x = 1

1

4to. 1ra. T. T. - Matemática Prof. Flavia Terrizzano

x

1 2) Sea f (x) =   . Hallar x: 2 f (x) + f (2) = f (1)

Rta. x = 2

3) Sea f(x) = 3x. Hallar x: [f (x)]2 + 9 . f (0) = 10 f (x)

Rta. x = 0 ó x = 2

4) Hallar x 10 x +1 =

0,1 10

Rta. x = −

x

Rta.

2

3 4

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