Question

os numeros reais nao nulos alfa e beta são tais que 2^alfa = 5^beta. nessas condicoes, podemos afirmar corretamente que o valor de alfa/beta é

Answer 1

$\mathsf{2^\alpha=5^\beta}$

$\mathsf{2^{\dfrac{\alpha}{\beta}}=5}$

$\mathsf{\log{2^{\dfrac{\alpha}{\beta}}}=\log5}$

$\mathsf{\dfrac{\alpha}{\beta}\log2=\log5}$

$\mathsf{\dfrac{\alpha}{\beta}=\dfrac{\log5}{\log2}}$

$\mathsf{\dfrac{\alpha}{\beta}=\dfrac{\log{\dfrac{10}{2}}}{\log2}}$

$\mathsf{\dfrac{\alpha}{\beta}=\dfrac{\log{10}-\log2}{\log2}}$

$\boxed{\mathsf{\log2\approx0,3}}$

$\mathsf{\dfrac{\alpha}{\beta}\simeq\dfrac{1-0,3}{0,3}}$

$\boxed{\mathsf{\dfrac{\alpha}{\beta}\simeq2,\overline{3}}}$

Answer 2

Boa noite Wellington

2^α  = 5^β

α*log(2) = β*log(5) 

α/β = log(5)/log(2) = (1 - log(2)/(log(2) = (1 - 0.3)/0.3 = 0.7/0.3 = 7/3 

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