Question

logaritmo calcule o valor de cada expressão

Answer 1

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$\large\boxed{\begin{array}{l}\rm a)~\sf \ell og_3\sqrt[\sf4]{\sf9}-4^{\ell og_45}\\\sf\ell og_{3^1}3^{\frac{1}{2}}-4^{\ell og_45}\\\sf=\dfrac{1}{2}-5=\dfrac{1-10}{2}=-\dfrac{9}{2}\end{array}}$

$\large\boxed{\begin{array}{l}\rm b)~\sf 2\ell og_91+\bigg[\ell og_{0,5}\bigg(\dfrac{1}{8}\bigg)\bigg]^2\\\sf=2\cdot0+\bigg[\ell og_{2^{-1}}2^{-3}\bigg]^2\\\sf=0+\bigg[\dfrac{-3}{-1}\bigg]^2\\\sf=3^2=9\end{array}}$

$\boxed{\begin{array}{l}\rm c)~\sf 6^{2+\ell og_67}-\ell og(\ell og10)\\\sf=6^2\cdot6^{\ell og_67}-\ell og(1)\\\sf=36\cdot7-0\\\sf=252\end{array}}$

$\large\boxed{\begin{array}{l}\rm d)~\sf4\ell og_82\sqrt{2}+\ell og_{\frac{1}{5}}0,04\\\sf= \ell og_{2^3}(2^{\frac{3}{2}})^4+\ell og_{5^{-1}}5^{-2}\\\sf=\ell og_{2^3}2^6+\ell og_{5^{-1}}5^{-2}\\\sf=\dfrac{6}{3}+\bigg[\dfrac{-2}{-1}\bigg]\\\sf=2+2=4\end{array}}$