Question

Encuentra el valor de x para que se cumpla la igualdad

Answer 1

Respuesta:

Explicación paso a paso:

$d) (\frac{\sqrt{13} }{\sqrt{5} } )^{x} = \frac{169}{25}$

$[\frac{(13)^{\frac{1}{2} } }{(5)^{\frac{1}{2} } } ]^{x} =[ \frac{13}{5}]^{2}$

$[( \frac{13}{5})^{\frac{1}{2} }]^{x} = [\frac{13}{5}]^{2}$

$(\frac{13}{5} )^{\frac{x}{2} } = (\frac{13}{5} )^{2}$

$\frac{x}{2} = 2$

$x = 2 ( 2 )$

$x = 4$

$e) (\frac{\sqrt{43} }{x} )^{3} = \frac{43}{49}$

$( \sqrt{43})^{3} * ( 49 ) = (x)^{3} * ( 43)$

$\frac{(\sqrt{43})^{3} * (49) }{43} = x^{3}$

$(43)^{\frac{3}{2} -1} * 49 = x^{3}$

$( 43)^{\frac{1}{2} } * 49 = x^{3}$

$\sqrt[3]{((\sqrt{43})(49))} = x$

$\sqrt[6]{43} * \sqrt[3]{49} = x$

$f) -6^{x} = -\frac{1}{36}$

$-(6)^{x} = - ( \frac{1}{36} )$

$- ( 6 )^{x} = - ( \frac{1}{6^{2} } )$

$- ( 6 )^{x} = - ( 6^{-2} )$

$(6)^{x} = (6^{-2} )$

$x = -2$

$g) ( -4 * \frac{1}{3} )^{x} = -\frac{64}{27}$

$(-\frac{4}{3} )^{x} = (-\frac{4}{3})^{3}$

$x = 3$