Question

Calcule as funções exponenciais:
a) 625^x=125
b) 81^x=243
c) 2^x+3=32^x+5
d)10x=10000
e)8^2x=16^x+2
f)9^x=27^x+3
g)5^x+5=25^2x+4

Answer 1

$a) (5^4)^x = 5^3 \ \textless \ \ \textgreater \ 4x=3\ \textless \ \ \textgreater \ x= 3/4 b)(3^4)^x=3^5 \ \textless \ \ \textgreater \ 4x=5\ \textless \ \ \textgreater \ x=5/4$

E assim por diante. Você tem que tentar igualar as bases para poder igualar os expoentes depois.

Answer 2

a) 625^x = 125
5^4x = 5^3
4x = 3
x = 3/4

b) 81^x = 243
3^4x = 3^5
4x = 5
x = 4/5

c) 2^x+3 = 32^x+5
2^x+3 = 2^5(x+5)
2^x+3 = 2^5x+25
x + 3 = 5x + 25
x - 5x = 25 - 3
-4x = 22
x = 22/-4
x = - 11/2

d) 10^x = 10000
10^x = 10^4
x = 4

e) 8^2x = 16^x+2
2^3.2x = 2^4(x+2)
3.2x = 4(x+2)
6x = 4x + 8
6x - 4x = 8
2x = 8
x = 8/2
x = 4

f) 9^x = 27^x+3
3^2x = 3^3(x+3)
3^2x = 3^9x+9
2x = 9x + 9
2x - 9x = 9
-7x = 9
x = - 7/9