Question

alguém poderia me ajudar!!

Answer 1

Resposta:

Explicação passo a passo:

$a)$

$2^{(x+7)} =\frac{1}{64}$

$2^{(x+7)} =2^{-6}$

$x+7=-6$

$x=-6-7$

$x=-13$

$b)$

$25^{x} =\sqrt{5}$

$5^{2x} =5^{\frac{1}{2} }$

  $2x=\frac{1}{2}$

   $x=\frac{1}{4}$

$c)$

$4^{x} =16$

$4^{x} =4^{2}$

$x=2$

$d)$

$(\frac{1}{9}) ^{x} =\sqrt{27}$

$3^{-2x} =\sqrt{3^{3} }$

$3^{-2x} =3^{\frac{3}{2} }$

 $-2x=\frac{3}{2}$

    $2x=-\frac{3}{2}$

      $x=-\frac{3}{4}$

$e)$

$49^{(2x+3)} =343$

$(7^{2}) ^{(2x+3)} =7^{3}$

 $7^{(4x+6)} =7^{3}$

   $4x+6=3$

   $4x=3-6$

     $4x=-3$

       $x=-\frac{3}{4}$

$f)$

  $9^{x} =1$

  $9^{x} =9^{0}$

   $x=0$

$g)$

$5^{x} =125$

$5^{x} =5^{3}$

 $x=3$

$h)$

$5^{(x-1)} +5^{(x+1)} =26$

$\frac{5^{x} }{5} +\:5^{x}\:.\:5 =26$

$Artificio=>5^{x}=y$

 $\frac{y}{5} +5y=26$

$Multiplicamos\;os\;dois\:membros\:por\;5\:ok!$

 $y+25y=130$

    $26y=130$

        $y=130/26$

        $y=5$

 $Voltemos\:ao\;artificio...$

       $5^{x}=y$

       $5^{x}=5$

       $5^{x} =5^{1}$

        $x=1$

$i)$

 $7^{(5x-9)} =7^{(-x+1)}$

  $5x-9=-x+1$

  $5x+x=1+9$

      $6x=10$

       $x=\frac{10}{6}$

        $x=\frac{5}{3}$

$j)$

  $(\frac{1}{4}) ^{x} =\frac{1}{16}$

  $(\frac{1}{4}) ^{x} =(\frac{1}{4}) ^{2}$

       $x=2$

$k)$

 $3^{x} =27$

 $3^{x} =3^{3}$

  $x=3$

$l)$

$2^{x} =\frac{1}{32}$

$2^{x} =\frac{1}{2^{5} }$

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

 $x=-5$

 

 

       

     

     

     

 

       

 

 

Answer 2

Explicação passo-a-passo:

A)

$2 {}^{x + 7} = \dfrac{1}{64}$

$2 {}^{x + 7} = 2 {}^{ - 6}$

$x + 7 = - 6$

$x = - 6 - 7$

x=>-13

B)

$25 {}^{x} = \sqrt{5}$

$5 {}^{2x} = 5 {}^{ \frac{1}{2} }$

$2x = \dfrac{1}{2}$

$2x \div 2 = \dfrac{1}{2} \times \dfrac{1}{2}$

x=>1/4

C)

$4 {}^{x} = 16$

$4 {}^{x} = 4 {}^{2}$

x=>2

D)

$( \dfrac{1}{9} ) {}^{x} = \sqrt{27}$

$3 {}^{ - 2x} = 3 {}^{ \frac{3}{2} }$

$- 2x = \dfrac{3}{2}$

$- 2x \div 2 = \dfrac{3}{2} \times \dfrac{1}{2}$

$- x = \dfrac{3}{4} ( - 1)$

x=>-3/4

E)

$49 {}^{2x + 3} = 343$

$7 {}^{4x + 6} = 7 {}^{3}$

$4x + 6 = 3$

$4x = 3 - 6$

$4x = - 3$

x=>-3/4

F)

$9 {}^{x} = 1$

$9 {}^{x} = 9 {}^{0}$

x=>0

G)

$5 {}^{x} = 125$

$5 {}^{x} = 5 {}^{3}$

x=>3

H)

$5 {}^{x - 1} + 5 {}^{x + 1} = 26$

$(1 + 5 {}^{2} ) \times 5 {}^{x - 1} = 26$

$(1 + 25) \times 5 {}^{x - 1} = 26$

$26 \times 5 {}^{x - 1} = 26$

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

$5 {}^{x - 1} = 5 {}^{0}$

$x - 1 = 0$

$x = 0 + 1$

x=>1

I)

$7 {}^{5x - 9} = 7 {}^{ - x + 1}$

$5x - 9 = - x + 1$

$5x + x = 1 + 9$

$6x = 10$

$x = \dfrac{10 {}^{ \div 2} }{6 {}^{ \div 2} }$

x=>5/3

J)

$( \dfrac{1}{4} ) {}^{x} = \dfrac{1}{16}$

$2 {}^{ - 2x} = 2 {}^{ - 4}$

$- 2x = - 4$

$x = \dfrac{ - 4}{ - 2}$

x=>2

K)

$3 {}^{x} = 27$

$3 {}^{x} = 3 {}^{3}$

x=>3

L)

$2 {}^{x} = \dfrac{1}{32}$

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

x=>-5