Question

determine o valor da expressão
Y = 3. log², ✓8 – 2· log½32+5.log ✓² 4

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Answer 1

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$\boxed{\begin{array}{l}\underline{\bf c\acute alculos~auxiliares\!:}\\\sf\ell og_2\sqrt{8}=\ell og_{2^1}2^{\frac{3}{2}}=\dfrac{\frac{3}{2}}{1}=\dfrac{3}{2}\\\sf \ell og_{\frac{1}{2}}32=\ell og_{2^{-1}}2^5=\dfrac{5}{-1}=-5\\\sf \ell og_{\sqrt{2}}4=\ell og_{2^{\frac{1}{2}}}2^2=\dfrac{2}{\frac{1}{2}}=2\cdot2=4\\\sf Y=3\cdot\ell og_2\sqrt{8}-2\cdot\ell og_{\frac{1}{2}}32+5\cdot\ell og_{\sqrt{2}}4\\\sf Y=3\cdot\dfrac{3}{2}-2\cdot(-5)+5\cdot4\\\sf Y=\dfrac{27}{2}+10+20\\\sf Y=\dfrac{27}{2}+30\end{array}}$

$\large\boxed{\begin{array}{l}\sf Y=\dfrac{27+60}{2}\\\sf Y=\dfrac{87}{2}\end{array}}\blue{\checkmark}$