Question

24^n+1=3^n+1.16 então log3 n e

Answer 1

(UPF) Se 24ⁿ⁺¹ = 3ⁿ⁺¹ · 16, então log₃ n é igual a:
a) −2
b) −1
c) 1/2d) 1
e) 2
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Calculando o valor de n:
$24^{n+1}=3^{n+1}\cdot16\\ \\\frac{24^{n+1}}{3^{n+1}}=16\\ \\\Big(\frac{24}{3}\Big)^{n+1}=16\\ \\(8)^{n+1}=16\\ \\(2^3)^{n+1}=2^4\\ \\2^{3n+3}=2^4\\ \\ \\3n+3=4\\ \\3n=4-3\\ \\3n=1\\ \\n=\frac{1}{3}$

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calculando o valor de log₃ n
$log_3 \ n=log_3 \ \frac{1}{3} =log_3 \ 3^{-1}=-1 \cdot log_3 \ 3=-1 \cdot 1=-1$

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Resposta correta: letra B