Question

1) Determine o conjunto verdade das equações exponenciais:
a) 2x= 64 b) 7x= 343


c) 5x = 125 d) 2x+2 = 64



e) 2x + 8 = 512 f) 2x+4 = 16

g) 2x+1 = 64 h) (2x)x = 16

Answer 1

Equação Exponencial

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• Letra A)

$\boxed{\begin{array}{lr} \\ \large \sf \: 2x = 64 \\ \\\large \sf 2x = {2}^{6} \\ \\ \large \sf \ \cancel 2x^{x} = \cancel{ {2}^{6}} \\ \\ \boxed{ \red{ \large \sf \: x = 6 }} \\ \: \end{array}}$

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• Letra B)

$\boxed{\begin{array}{lr} \\ \large \sf \: 7x = 343 \\ \\ \large \sf \:7x = {7}^{3} \\ \\ \large \sf \cancel{7x^{x}} = \cancel{ {7}^{3}} \\ \\ \boxed{ \red{\large \sf x = 3}} \\ \: \end{array}}$

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• Letra C)

$\boxed{\begin{array}{lr} \\ \large \sf \sf5x = 125 \\ \\ \large \: \sf 5x = {5}^{3} \\ \\ \large \sf \: \cancel{ 5x^{x} }= \cancel{5}^{3} \\ \\ \boxed{ \red{\large \sf \: x = 3}} \\ \: \end{array}}$

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• Letra D)

$\boxed{\begin{array}{lr} \\ \large \sf \: {2}^{x + 2} = 64 \\ \\ \large \sf \: {2}^{x + 2} = {2}^{6} \\ \\ \large \sf \cancel{{2}}^{x + 2} = \cancel{ {2}}^{6} \\ \\ \large \sf x + 2 = 6 \\ \\ \large \sf x = 6 - 2 \\ \\ \boxed{ \red{ \large \sf x = 4}} \\ \: \end{array}}$

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• Letra E)

$\boxed{\begin{array}{lr} \\ \: \large \sf{2}^{x + 8} = 512 \\ \\ \large \sf{2}^{x + 8} = {2}^{9} \\ \\\large \sf \cancel{ {2}}^{x + 8} = \cancel{ {2}}^{9} \\ \\ \large \sf \: x + 8 = 9 \\ \\ \large \sf \: x = 9 - 8 \\ \\ \boxed{ \red{\large \sf x = 1}} \\ \: \end{array}}$

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• Letra F)

$\boxed{\begin{array}{lr} \\ \large \sf \: {2}^{x + 4} = 16 \\ \\ \large \sf \: {2}^{x + 4} = {2}^{4} \\ \\ \large \sf \cancel{ {2}}^{x + 4} = \cancel{{2}}^{4} \\ \\\large \sf x + 4 = 4 \\ \\ \large \sf \: x = 4 - 4 \\ \\ \boxed{ \red{\large \sf x = 0}} \\ \: \end{array}}$

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• Letra G)

$\boxed{\begin{array}{lr} \\ \large \sf \: {2}^{x + 1} = 64 \\ \\\large \sf \: {2}^{x + 1} = {2}^{6} \\ \\ \large \sf \cancel{{2}}^{x + 1} = \cancel{ {2}}^{6} \\ \\\large \sf \: x + 1 = 6 \\ \\ \large \sf \: x = 6 - 1 \\ \\ \boxed{ \red{\large \sf \: x = 5}} \\ \: \end{array}}$

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• Letra H)

$\boxed{\begin{array}{lr} \\ \large \sf {2}^{{x}^{2}}= 16 \\ \\ \large \sf{2}^{{x}^2}} = {2}^{4} \\ \\ \large \sf \cancel{{2}}^{x} = \cancel{{2}}^{4} \\ \\ \boxed{ \red{ \large \sf {x}^{2}=4}} \\ \: \end{array}}$

Equação do Segundo Grau Incompleta:

$\boxed{\begin{array}{lr} \\ \large \sf {x}^{2} \\ \\ \large \sf x = \pm \sqrt{4} \\ \\ \boxed{ \red{ \large \sf x = \pm 2 }} \\ \: \end{array}}$

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