Question

Logaritimo de 3 raiz de 3 na base 27 ?

Answer 1

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

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

$( 3^{3} )^{x} = 3 \sqrt{3}$

$3^{3x} = \sqrt{3.( 3)^{2} }$

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

$3^{3x} = 27^{ \frac{1}{2} }$

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

3x = $\frac{3}{2}$

x = $\frac{ \frac{3}{2} }{3}$

x = $\frac{3}{2} . \frac{1}{3}$

x = $\frac{1}{2}$

Answer 2

$log _{27} 3 \sqrt{3}$

$27^{x} = 3 \sqrt{3}$
$(3.9)^x= 3. 3^{1/2}$
$(3.9)^x= 3^{3/2}$
$(3.3^2)^x= 3^{3/2}$
$( 3^{3} )^x= 3^{3/2}$

$3x= 3/2$
$x= 3/6$
$x= 1/2$