Question

Se log2 a = 2 e log2 b = √3, então, qual o valor de log2 (ab) √2?

Answer 1

$\mathsf{log_{2}(ab)\sqrt{2}=log_{2}a+log_{2}b+log_{2}\sqrt{2}}\\\mathsf{log_{2}a+log_{2}b+log_{2}2^{\frac{1}{2}}}\\\mathsf{log_{2}a+log_{2}b+\dfrac{1}{2}log_{2}2}\\\mathsf{2+\sqrt{3}+\dfrac{1}{2}=\dfrac{4+2\sqrt{3}+1}{2}}\\\huge\boxed{\boxed{\boxed{\boxed{\mathsf{\dfrac{5+2\sqrt{3}}{2}}}}}}$

Answer 2

Resposta:

2 + √6

Explicação passo a passo:

(Ufla-MG) Se log2 a = √2 e log2 b = √3, então, qual o valor de ^√2?

√2*log2 (ab)

√2*(log2 (a)+log2 (b))

√2 *(√2 + √3)

√4 + √6

2 + √6