Question

4) Sabendo que log 2 =a e log 3 = b, calcule, em
função de a e b, o valor de log
$\sqrt[3]{12}$
​

Answer 1

Resposta:

log∛12=(2a+b)/3

Explicação passo-a-passo:

log∛12=log(12)¹⁺³=1/3.log12=1/3.log4.3=1/3(log4+log3)=1/3(log2²+log3)=

1/3(2.log2+log3)=1/3(2.a+b)

Answer 2

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$\sf\ell og\sqrt[\sf3]{\sf12}=\ell og\sqrt[\sf3]{\sf 2^2\cdot 3}=\ell og\sqrt[\sf3]{\sf 2^2}\cdot\sqrt[\sf3]{\sf3}\\\sf\ell og\sqrt[\sf3]{\sf12}=\ell og\sqrt[\sf3]{\sf2^2}+\ell og\sqrt[\sf3]{\sf3}=\ell og2^{\frac{2}{3}}+\ell og3^{\frac{1}{3}}\\\sf\ell og\sqrt[\sf3]{\sf12}=\frac{2}{3}\ell og2+\dfrac{1}{3}\ell og3\\\huge\boxed{\boxed{\boxed{\boxed{\sf\ell og\sqrt[\sf3]{\sf12}=\dfrac{2a+b}{3}}}}}\blue{\checkmark}$