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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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[tex]\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\rm log_b(a) = c \iff b^c = a}&\\&&\\\end{array}}}}}[/tex]
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[tex]\text{\pink{$\Longrightarrow$}~\Large\orange{$\sf a$}}[/tex] sendo o logaritmando de tal forma que a > 0;
[tex]\text{\pink{$\Longrightarrow$}~\Large\orange{$\sf b$}}[/tex] sendo a base de tal forma que b > 0 e b ≠ 1;
[tex]\text{\pink{$\Longrightarrow$}~\Large\orange{$\sf c$}}[/tex] sendo o logaritmo.
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⠀⠀Sendo assim temos que:
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[tex]\LARGE\blue{\text{$\sf~c)~log_{\sqrt{2}} (x) = 5 $}}[/tex]
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[tex]\LARGE\blue{\text{$\sf (\sqrt{2})^5 = x$}}[/tex]
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[tex]\LARGE\blue{\text{$\sf (2^{\frac{1}{2}})^5 = x$}}[/tex]
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[tex]\LARGE\blue{\text{$\sf 2^{\frac{5}{2}} = x$}}[/tex]
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[tex]\LARGE\blue{\text{$\sf 2^{\frac{4}{2} + \frac{1}{2}} = x$}}[/tex]
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[tex]\LARGE\blue{\text{$\sf 2^{\frac{4}{2}} \cdot 2^{\frac{1}{2}} = x$}}[/tex]
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[tex]\LARGE\blue{\text{$\sf 2^2 \cdot \sqrt{2} = x$}}[/tex]
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[tex]\LARGE\blue{\text{$\sf x = 4 \cdot \sqrt{2}$}}[/tex]
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[tex]\huge\green{\boxed{\rm~~~\gray{x}~\pink{=}~\blue{ 4 \cdot \sqrt{2} }~~~}}[/tex] ✅
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[tex]\LARGE\blue{\text{$\sf~f)~log_{2/3} (x) = 3 $}}[/tex]
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[tex]\LARGE\blue{\text{$\sf \left(\dfrac{2}{3}\right)^3 = x $}}[/tex]
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[tex]\LARGE\blue{\text{$\sf \dfrac{2^3}{3^3} = x $}}[/tex]
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[tex]\LARGE\blue{\text{$\sf x = \dfrac{8}{27} $}}[/tex]
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[tex]\huge\green{\boxed{\rm~~~\gray{x}~\pink{=}~\blue{ \dfrac{8}{27} }~~~}}[/tex] ✅
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[tex]\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
⠀⠀☀️ Veja mais exercícios sobre funções logarítmicas:
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✈ https://brainly.com.br/tarefa/37959466
✈ https://brainly.com.br/tarefa/38073488
✈ https://brainly.com.br/tarefa/37919054
✈ https://brainly.com.br/tarefa/38001308
[tex]\bf\large\red{\underline{\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}[/tex]✍
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[tex]\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]☁
⠀⠀⠀⠀☕ [tex]\Large\blue{\text{\bf Bons~estudos.}}[/tex]
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([tex]\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}[/tex]) ☄
[tex]\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX[/tex]✍
❄☃ [tex]\sf(\purple{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})[/tex] ☘☀
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[tex]\Huge\green{\text{$\underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~}$}}[/tex] ✞
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