Materi persamaan eksponensial berbentuk.Ini bagaimana caranya?

Persamaan Ekponen
bentuk h(x)^f(x) = h(x)^g(x)

1) (x – 7)ˣ² ⁻²  = (x – 7)ˣ
h(x) = x-7
f(x) = x² – 2
g(x) = x

a) f(x) = g(x)
x² – 2 = x –> x² – x  – 2= 0
(x – 2)(x + 1) = 0
x = 2 atau x = – 1

b) h(x) = 1
x – 7 = 1 –> x = 6

c) h(x)= 0 , jika   f(x) ,g(x) > 0
x – 7 = 0
x = 7
f(7) = 7² – 2 = 47 –> f(7) > 0
g(7) = 7 –> g(7) > 0

d)  h(x) = – 1 , jika f(x), g(x) keduanya ganjil atau keduanya genap
x – 7 = -1
x = – 6
f(-6) = (-6)² – 2 = 34 –> f(-6)  genap
g(-6) = -6  –> g(-6)  genap

HP x = (-6, – 1 , 2 , 7, 8 )

2) (2x-5)ˣ²⁺¹ = (2x-5)ˣ⁺⁷
h(x) = 2x -5
f(x)= x² + 1
g(x)= x + 7
a)  f(x) = g(x)
x² + 1 = x + 7
x² – x – 6 = 0
(x – 3)(x +2)= 0
x = 3 atau x = – 2

b) h(x)= 1
2x-5 = 1
x = 3

c) h(x) =0
2x -5 = 0
x = 5/2
f(5/2) = (5/2)² + 1 = 7 1/4  –> f(5/2)  > 0
g(5/2) = 5/2 + 7 = 9 1/2 –> g(5/2) > 0

d) h(x) =  -1
2x – 5 = – 1
x = 2
f(2) = 2² + 1 = 5 –> f(2)  gnjil
g(2) = 2 +7 = 9 –> g(2) ganjil

HP x = (-2,  2 , 5/2 , 3)