Question

resolva as equações exponenciais a) 729^2x=27

b)(1/4)^4x=0.25

Answer 1

Explicação passo-a-passo:

$729^{2x}=27\\ \\ fatorando\\ \\ (3^6)^{2x}=3^3\\ \\ 3^{12x}=3^3\\ \\ cancela~~as~~bases\\ \\ 12x=3\\ \\ x={3\over12}~~~simplificando\\ \\ x={1\over4}$

$b)\\ \\ ({1\over4})^{4x}=0,25\\ \\ ({1\over4})^{4x}={25\over100}\\ \\ ({1\over4})^{4x}=({1\over4})^1\\ \\ 4x=1\\ \\ x={1\over4}$

Answer 2

a) 729²ˣ = 27

(3⁶)²ˣ = 3³

3¹²ˣ = 3³

12x = 3

x = 3/12

x= 1/4

b) ( 1/4 )⁴ˣ = 0,25

( 1/4 )⁴ˣ = ( 25/100 )

( 1/4) ⁴ˣ = ( 1/4 )¹

4x = 1

x = 1/4