Question

PORFAVOR AJUDA PRA HOJE AINDA!!!!!

1. Usando a definição, calcule o valor dos seguintes logaritmos:
a) log2 16 =
b) log3 81 =
c) log5 125 =
d) log36 √6 =
e) log√3 3 =

3. Qual é o valor de x em:
a. log3 x = 4
b. logx 2 = 1
c. logx 0,25 = −1

Answer 1

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1)

$\tt a)~\sf\ell og_216=x\Longleftrightarrow 2^x=16\\\sf 2^x=2^4\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=4\checkmark}}}}$

$\tt b)~\sf\ell og_381=x\Longleftrightarrow 3^x=81\\\sf 3^x=3^4\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=4\checkmark}}}}$

$\tt c)~\sf\ell og_5125=x\Longleftrightarrow 5^x=125\\\sf 5^x=5^3\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=3\checkmark}}}}$

$\tt d)~\sf\ell og_{36}\sqrt{6}=x\Longleftrightarrow 36^x=\sqrt{6}\\\sf 6^{2x}=6^{\frac{1}{2}}\\\sf 2x=\dfrac{1}{2}\implies 4x=1\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=\dfrac{1}{4}\checkmark}}}}$

$\tt e)~\sf\ell og_{\sqrt{3}}3=x\Longleftrightarrow (\sqrt{3})^x=3\\\displaystyle\sf 3^{\frac{x}{2}}=3^1\\\sf \dfrac{x}{2}=1\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=2\checkmark}}}}$

2)

$\tt a)~\sf\ell og_55+\ell og_31-\ell og10=\diagup\!\!\!1+0-\diagup\!\!\!1=0\checkmark\\\tt b)~\sf\ell og_{\frac{1}{4}}4+\ell og_4{\frac{1}{4}}=\ell og_{2^{-2}}2^2+\ell og_{2^2}2^{-2}\\\sf\ell og_{\frac{1}{4}}4+\ell og_4\frac{1}{4}=\dfrac{2}{-2}+\dfrac{-2}{2}=-1-1=-2\checkmark$

3)

$\tt a)~\sf\ell og_3x=4\Longleftrightarrow x=3^4=81\checkmark\\\tt b)~\sf\ell og_x2=1\Longleftrightarrow x=2\checkmark\\\tt c)~\sf\ell og_x0,25=-1\Longleftrightarrow x^{-1}=0,25\\\sf x^{-1}=\dfrac{1}{4}\\\sf\dfrac{1}{x}=\dfrac{1}{4}\\\huge\boxed{\boxed{\boxed{\boxed{\sf x=4\checkmark}}}}$