Question

Resolva as seguintes equações exponenciais na variavel x
a) 2^x = 64
b) 3^x-2= 9
c) 5^x2 - ^x2 = 125
d) 10^1-^x =1/10
e) 2^4x-^x2= 8
f) (10^x)^1-x= 0,000001
g) 3^2 -x = 1/27
h) 3^x-5= 27^1-x

Answer 1

a)
MMC ( 64 ) = 2^6
64 | 2
32 | 2
16 | 2
8 | 2
4 | 2
2 | 2

2× = 2^6
x = 6
________________________
b)
3^x-2 = 3^2
x - 2 = 2
x = 4
______________
c)
5^ x2 - x2 = 5^3
2x - 2 x = 3
0x = 3
x = 0
_____________
d)
10^1-x = 10 ^ -1
1 - x = - 1
x = 0
_____________
e)
2^ 4x-x2 = 2^3
4 x - 2 x = 3
2 x = 3
x = 3/2
______________
f)
10^1x-x2 = 10^6
x² - x = 6
x² - x - 6 = 0
x’ = - 3 x'' = 2
_______________
g)
3^2-x = 3 ^ - 3
2 - x = - 3
x = 1
________________
h)
3 ^ x-5 = 3 ^ 3 - 3 x
x - 5 = 3 - 3 x
4 x = 8
x = 8/4
x = 2