A)Dados X=㏑10 Calcule Y e²ˣ+e⁻ˣ=Y B) Dado In3= X calcule Y ㏑9+㏑27x=Y.... Pergunta de ideia deNooel

January 2020 1 76 Report

A)Dados X=㏑10 Calcule Y

e²ˣ+e⁻ˣ=Y

B) Dado In3= X calcule Y

㏑9+㏑27x=Y

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superaks

Verified answer

Olá Spawwn.

Propriedades logarítmicas usadas:

$\star~\boxed{\boxed{\mathsf{\ell n(a)\Rightarrow \ell og_e(a)}}}\\\\\\\star~\boxed{\boxed{\mathsf{\ell og_b(a)=\ell og_b(a)~\Rightarrow~ b^{\ell og_b(a)}=a}}}$

A -

Organizando e resolvendo:

$\mathsf{x=\ell n(10)}\\\\\\\mathsf{y=e^{2x}+e^{-x}}\\\\\mathsf{y=e^{2\cdot\ell n(10)}+e^{-\ell n(10)} }\\\\\mathsf{y=e^{\ell n(10^2)}+e^{\ell n(10^{-1})}}\\\\\mathsf{y=10^2+10^{-1}}\\\\\mathsf{y=100+\dfrac{1}{10}}\\\\\mathsf{y=\dfrac{1.000+1}{10}}\\\\\boxed{\mathsf{y=\dfrac{1.001}{10}}}$

B -

$\mathsf{\ell n(3)= x}\\\\\\\mathsf{y=\ell n(9)+\ell n(27x)}\\\\\mathsf{y=\ell n(3^2)+\ell n(3^3\cdot x)}\\\\\mathsf{y=2\cdot \ell n(3)+3\cdot\ell n(3)+\ell n(x)}\\\\\mathsf{y=2x+3x+\ell n(x)}\\\\\boxed{\mathsf{y=5x+\ell n(x)}}$

Dúvidas? comente.

2 votes Thanks 1

Nooel Obg

superaks :D