Question

Pois podes por a Resposta
Log√2 x=5

Log2/3 x=3

É Se estás aqui Jesus Cristo te ama e eu também

Answer 1

Resposta:

Explicação passo-a-passo:

Answer 2

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⠀⠀☞ Tendo manipulado algebricamente as funções log encontramos que: a) x = 4 × √2; b) x = 8/27. ✅

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⚡ " -O que significa 'log'?"

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⠀⠀Log é a abreviação de logaritmo, que é a notação para a função logarítmica que opera com os expoentes de potências de forma que:

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm log_b(a) = c \iff b^c = a}&\\&&\\\end{array}}}}}$

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$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf a }}$ sendo o logaritmando de tal forma que a > 0;

$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf b }}$ sendo a base de tal forma que b > 0 e b ≠ 1;

$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf c }}$ sendo o logaritmo.

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⠀⠀Sendo assim temos que:

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$\LARGE\blue{\text{ \sf~c)~log_{\sqrt{2}} (x) = 5 }}$

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$\LARGE\blue{\sf (\sqrt{2})^5 = x}$

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$\LARGE\blue{\text{ \sf (2^{\frac{1}{2}})^5 = x }}$

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$\LARGE\blue{\text{ \sf 2^{\frac{5}{2}} = x }}$

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$\LARGE\blue{\text{ \sf 2^{\frac{4}{2} + \frac{1}{2}} = x }}$

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$\LARGE\blue{\text{ \sf 2^{\frac{4}{2}} \cdot 2^{\frac{1}{2}} = x }}$

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$\LARGE\blue{\sf 2^2 \cdot \sqrt{2} = x}$

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$\LARGE\blue{\sf x = 4 \cdot \sqrt{2}}$

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$\huge\green{\boxed{\rm~~~\gray{x}~\pink{=}~\blue{ 4 \cdot \sqrt{2} }~~~}}$ ✅

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$\LARGE\blue{\sf~f)~log_{2/3} (x) = 3 }$

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$\LARGE\blue{\sf \left(\dfrac{2}{3}\right)^3 = x }$

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$\LARGE\blue{\sf \dfrac{2^3}{3^3} = x }$

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$\LARGE\blue{\sf x = \dfrac{8}{27} }$

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$\huge\green{\boxed{\rm~~~\gray{x}~\pink{=}~\blue{ \dfrac{8}{27} }~~~}}$ ✅

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$

⠀⠀☀️ Veja mais exercícios sobre funções logarítmicas:

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✈ https://brainly.com.br/tarefa/37959466

✈ https://brainly.com.br/tarefa/38073488

✈ https://brainly.com.br/tarefa/37919054

✈ https://brainly.com.br/tarefa/38001308

$\bf\large\red{\underline{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

⠀⠀⠀⠀☕ $\Large\blue{\text{\bf Bons~estudos.}}$

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($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

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