Question

Aplicando os conhecimentos adquiridos nas aula ministradas, determine o valor da seguinte expressão: Log5 625 + Log 100 - Log3 27 + Log 10 – Log2 16 . ​

Answer 1

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☞ O valor da expressão é -1. ✅

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$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

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☔ Oi, Rogerio. Inicialmente  lembremos 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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☔ Com isto podemos encontrar o valor para cada um dos termos da nossa expressão:

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$\LARGE\blue{\sf log_5(625) = x }$

⠀⠀  $\LARGE\blue{\sf 5^x = 625 }$

⠀⠀  $\LARGE\blue{\sf 5^x = 5^4 }$

⠀⠀  $\LARGE\blue{\sf x = 4 }$

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$\LARGE\blue{\sf log_{10}(100) = x }$

⠀⠀  $\LARGE\blue{\sf 10^x = 100 }$

⠀⠀  $\LARGE\blue{\sf 10^x = 10^2 }$

⠀⠀  $\LARGE\blue{\sf x = 2 }$

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$\LARGE\blue{\sf log_3(27) = x }$

⠀⠀  $\LARGE\blue{\sf 3^x = 27 }$

⠀⠀  $\LARGE\blue{\sf 3^x = 3^3 }$

⠀⠀  $\LARGE\blue{\sf x = 3 }$

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$\LARGE\blue{\sf log_{10}(10) = x }$

⠀⠀  $\LARGE\blue{\sf 10^x = 10 }$

⠀⠀  $\LARGE\blue{\sf x = 1 }$

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$\LARGE\blue{\sf log_2(16) = x }$

⠀⠀  $\LARGE\blue{\sf 2^x = 16 }$

⠀⠀  $\LARGE\blue{\sf 2^x = 2^4 }$

⠀⠀  $\LARGE\blue{\sf x = 4 }$

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☔ Reescrevendo nossa função temos:

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$\LARGE\blue{\sf 4 + 2 - 4 + 1 - 4 = -1 }$

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$\Huge\green{\boxed{\rm~~~\blue{ -1 }~~~}}$ ✅

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

☕ $\bf\Large\blue{Bons\ estudos.}$

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

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

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

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$