Question

Resouva em IR as equações exponenciais

a)$8^{x}=64$

b)$5^2x-1= \frac{1}{5}$

c)4x=0,25

d)$27^3-x= \frac{1}{81}$

e)$(\frac{2}{3})^3x+1=1$

Answer 1

a) 8^x = 64

8^x = 8^2

x = 2

b) 5^(2x-1) = 1/5

5^(2x-1) = 5^(-1)

2x-1 = -1
2x = -1+1
2x = 0 

x = 0

c) 4^x = 0,25

4^x = 1/4
4^x = 4^(-1)

x = -1

d) 27^(3-x) = 1/81

3^[3(3-x)] = 1/3^4
3^[3(3-x)] = 3^(-4)

9 - 3x = -4
-3x = -13

x = 13/3

e) (2/3)^(3x+1) = 1

(2/3)^(3x+1) = (2/3)^0

3x+1=0
3x = -1

x = -1/3