Question

Se A = log2 (128)⁵ e B = log2 1/512. Qual é o valor de A - B?

a) 35
b) - 35
c) 44
d) - 43
e) 70​

Answer 1

$\log_ab-\log_ac=\log_a(\frac{b}{c})\\\\\log_a(a^b)=b\\\\(a^b)^c=a^{bc}\\\\a^b.a^c=a^{b+c}$

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$\log_{2}(128)^5-\log_{2}\frac{1}{512}\\\\\log_2(\frac{128^5}{\frac{1}{512}})\\\\\log_{2}(128^5.512)\\\\\log_{2}((2^7)^5.2^9)\\\\\log_{2}(2^{35}.2^9)\\\\\log_{2}(2^{44})\\\\44$

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{A = log_2\:(128)^5}$

$\mathsf{A = log_2\:(2^7)^5}$

$\mathsf{A = log_2\:(2)^{35}}$

$\mathsf{A = 35}}$

$\mathsf{B = log_2\:\left(\dfrac{1}{512}\right)}$

$\mathsf{B = log_2\:\left(\dfrac{1}{2^9}\right)}$

$\mathsf{B = log_2\:2^{-9}}$

$\mathsf{B = -9}$

$\mathsf{A - B = 35 - (-9)}$

$\mathsf{A - B = 35 + 9}$

$\boxed{\boxed{\mathsf{A - B = 44}}}\leftarrow\textsf{letra C}$