Question

qual o logaritmo √3 na base 27?

Answer 1

$log_{27}\sqrt3=x\Rightarrow 27^x=\sqrt3\\ \\ (3^3)^x=3^{\frac{1}{2}}\\ \\ 3^{3x}=3^{\frac{1}{2}}\\ \\ 3x=\frac{1}{2}\\ \\ x=\frac{1}{6}$

Answer 2

$\text{log}_{27}\sqrt{3}=k$, então $27^{k}=\sqrt{3}$

$(3^3)^{k}=3^{\frac{1}{2}}$

$3^{3k}=3^{\frac{1}{2}}$

$3k=\dfrac{1}{2}$

$k=\dfrac{1}{6}$