Question

Determine as raizes das funções?


a) f(x) = 100ˣ = 0,001
b) f(x) = 8^(5x² - 3x - 2) = 1
c) f(x) = (√3)³= 9
d) f(x) = ($\frac{9}{16}$)^(x-3) = ($\frac{12}{9}$)ˣ

Answer 1

Vamos là

a) f(x) = 100^x = 0.001

10^(2x) = 10^-3

2x = -3.  x = -3/2

b) f(x) = 8^(5x² - 3x - 2) = 1

8^(5x² - 3x - 2) = 8^0

5x² - 3x - 2 = 0

d² = 9 + 40 = 49, d = 7

x1 = (3 + 7)/10 = 1.  x2 = (3 - 7)/10 = -2/5

c) f(x) = (√3)^x= 9

3^(x/2) = 3^2

x/2 = 2, x = 4

d) f(x) = (9/16)^(x-3) = ({12/9)^x

(3/4)^(2x - 6) = (3/4)^-x

2x - 6 = -x,  3x = -6, x = -2