Question

Me ayudan por favor amigos es urgente ​

Answer 1

Respuesta:

Hola!!

Explicación paso a paso:

La primera :

$4 ^{x} =6 {}^{1 - x}$

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

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

$2x + log_{2}(6)x = log_{2}(6)$

$(2 + log_{2}(6))x = log_{2}(6)$

$x = \frac{ log_{2}(6) }{2 + log_{2}(6) }$

$x = \frac{ log_{2}(6) }{ log_{2}(2^{2}) + log_{2}(6) }$

$x = \frac{ log_{2}(6) }{ log_{2}(2 ^{2} \times 6) }$

$x = \frac{ log_{2}(6) }{ log_{2}(4 \times 6) }$

$x = \frac{ log_{2}(6) }{ log_{2}(24) }$

$x = log_{24}(6)$

$x = 0.563791$

y la segunda:

$5^{3x - 1} = 3 ^{1 - 2x}$

$3x - 1 = log_{5}(3) - 2 log_{5}(3)x$

$3x + 2 log_{5}(3)x = log_{5}(3) + 1$

$(3 + 2 log_{5}(3))x = log_{5}(3) + 1$

$= \frac{ log_{5}(3) + 1}{3 + 2 log_{5}(3) }$

$x = \frac{ log_{5}(3) + log_{5}(5) }{ log_{5}(5 {}^{3} ) + log_{5}(3 {}^{2} ) }$

$x = \frac{ log_{5}(15) }{ log_{5}(5 ^{3} \times 3 {}^{2} ) }$

$x = \frac{ log_{5}(15) }{ log_{5}(125 \times 9) }$

$x = \frac{ log_{5}(15) }{ log_{5}(1125) }$

$x = log_{1125}(15)$

$x = 0.385458$

y la tercera :

$3 ^{x} . \: 7 {}^{x} = 22$

$(3 \times 7) {}^{x} = 22$

$21 {}^{x} = 22$

$x = log_{21}(22)$

$x = 1.01528$

suerte!!