Explicação passo-a-passo:
A)
[tex]2 {}^{x + 7} = \dfrac{1}{64} [/tex]
[tex]2 {}^{x + 7} = 2 {}^{ - 6} [/tex]
[tex]x + 7 = - 6[/tex]
[tex]x = - 6 - 7[/tex]
x=>-13
B)
[tex] 25 {}^{x} = \sqrt{5} [/tex]
[tex]5 {}^{2x} = 5 {}^{ \frac{1}{2} } [/tex]
[tex]2x = \dfrac{1}{2} [/tex]
[tex]2x \div 2 = \dfrac{1}{2} \times \dfrac{1}{2} [/tex]
x=>1/4
C)
[tex]4 {}^{x} = 16[/tex]
[tex]4 {}^{x} = 4 {}^{2} [/tex]
x=>2
D)
[tex]( \dfrac{1}{9} ) {}^{x} = \sqrt{27} [/tex]
[tex]3 {}^{ - 2x} = 3 {}^{ \frac{3}{2} } [/tex]
[tex] - 2x = \dfrac{3}{2} [/tex]
[tex] - 2x \div 2 = \dfrac{3}{2} \times \dfrac{1}{2} [/tex]
[tex] - x = \dfrac{3}{4} ( - 1)[/tex]
x=>-3/4
E)
[tex]49 {}^{2x + 3} = 343[/tex]
[tex]7 {}^{4x + 6} = 7 {}^{3} [/tex]
[tex]4x + 6 = 3[/tex]
[tex]4x = 3 - 6[/tex]
[tex]4x = - 3[/tex]
x=>-3/4
F)
[tex]9 {}^{x} = 1[/tex]
[tex]9 {}^{x} = 9 {}^{0} [/tex]
x=>0
G)
[tex]5 {}^{x} = 125[/tex]
[tex]5 {}^{x} = 5 {}^{3} [/tex]
x=>3
H)
[tex]5 {}^{x - 1} + 5 {}^{x + 1} = 26[/tex]
[tex](1 + 5 {}^{2} ) \times 5 {}^{x - 1} = 26[/tex]
[tex](1 + 25) \times 5 {}^{x - 1} = 26[/tex]
[tex]26 \times 5 {}^{x - 1} = 26[/tex]
[tex]5 {}^{x - 1} = 1[/tex]
[tex]5 {}^{x - 1} = 5 {}^{0} [/tex]
[tex]x - 1 = 0[/tex]
[tex]x = 0 + 1[/tex]
x=>1
I)
[tex]7 {}^{5x - 9} = 7 {}^{ - x + 1} [/tex]
[tex]5x - 9 = - x + 1[/tex]
[tex]5x + x = 1 + 9[/tex]
[tex]6x = 10[/tex]
[tex]x = \dfrac{10 {}^{ \div 2} }{6 {}^{ \div 2} } [/tex]
x=>5/3
J)
[tex]( \dfrac{1}{4} ) {}^{x} = \dfrac{1}{16} [/tex]
[tex]2 {}^{ - 2x} = 2 {}^{ - 4} [/tex]
[tex] - 2x = - 4[/tex]
[tex]x = \dfrac{ - 4}{ - 2} [/tex]
x=>2
K)
[tex]3 {}^{x} = 27[/tex]
[tex]3 {}^{x} = 3 {}^{3} [/tex]
x=>3
L)
[tex]2 {}^{x} = \dfrac{1}{32} [/tex]
[tex]2 {}^{x} = 2 {}^{ - 5} [/tex]
x=>-5
