Question

me ajudem na equações exponenciais

a) 225^x = raiz de 15
b) (0,3)^×-5 = 3/10
c) (1/4)^x = 128​

Answer 1

Resposta:

A) x=1/4  B) x=6  C) x=-7/2

Explicação passo-a-passo:

A) 225^x  = √15

    [(15²)^x]² = 15 >> 15^4x = 15 >> 4x = 1 >> x = 1/4

B) (0,3)^x-5 = 3/10

    (0,3)^x-5 = 0,3 >> x-5 = 1 >> x = 6

C) (1/4)^x = 128

   (4^-1)^x = 2^7

   2^-2x = 2^7 >> -2x = 7 >> x = -7/2

Answer 2

Resposta:

$a)\\ 225^x=\sqrt{15} \\ \\ (15^2)^x=15^{{1\over2}}\\ \\ 15^{2x}=15^{{1\over2}}\\ \\ cancela~~a~~base\\ \\ 2x={1\over2}\\ \\ 4x=1\\ \\ x={1\over2}\\ \\ S=\{{1\over2}\}$

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$b)\\ (0,3)^{x-5}={3\over10}\\ \\ Sendo~~{3\over10}=0,3\\ \\ (0,3)^{x-5}=0,3^1\\ \\ x-5=1\\ \\ x=1+5\\ \\ x=6\\ \\ S=\{6\}$

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$c)\\ ({1\over4})^x=128\\ \\ ({1\over2^2})^x=128\\ \\ (2^{-2})^x=128\\ \\ 2^{-2x}=2^7\\ \\ -2x=7~~~\times(-1)\\ \\ 2x=-7\\ \\ x=-{7\over2}\\ \\ S=\{-{7\over2}\}$