Question

qual o logaritmo √3 na base 27?

Answer 1

$\mathsf{\ell og_{27}(\sqrt{3})=x}\\\\\mathsf{27^x=\sqrt{3}}\\\mathsf{(3^3)^x=3^{\frac{1}{2}}}\\\\\mathsf{3x=\dfrac{1}{2}}\\\\\mathsf{x=\dfrac{1}{3}\cdot\dfrac{1}{2}}\\\\\\\boxed{\mathsf{x=\dfrac{1}{6}}}$

Dúvidas? comente

Answer 2

㏒ $\sqrt{3}$
    27                         = x

$27^{x} = \sqrt{3}$

se eu for rescrever essa raiz usando o " sol sombra, sombra sol "
fica:
27^{x} = 3^{1/2}

27  = (3^{3})^x

então 
(3^{x})^3 = 3^{1/2}
x =1/6