Question

1)Resolva s equações exponencias:
${2}^{2x + 1} = 16$
${6}^{5x - 2} = 36$
${125}^{x + 1} = \frac{1}{5}$
${7}^{3x - 6} = 49$
${9}^{7x + 3} = 729$
${3}^{4x + 10} = \frac{1}{81}$




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Answer 1

Resposta:

${2}^{2x + 1} = 16 \\ \\ {2}^{2x + 1} = {2}^{4} \\ \\ 2x + 1 = 4 \\ \\ 2x = 4 - 1 \\ \\ 2x = 3 \\ \\ x = \frac{3}{2}$

________//_______//_____

${6}^{5x - 2} = 36 \\ \\ {6}^{5x - 2} = {6}^{2} \\ \\ 5x - 2 = 2 \\ \\ 5x = 2 + 2 \\ \\ 5x = 4 \\ \\ x = \frac{4}{5}$

_______//___________//____

${125}^{x + 1} = \frac{1}{5} \\ \\ ( {(5)}^{3} ) {}^{x + 1} = {5 }^{ - 1} \\ \\ {5}^{3x + 3} = {5}^{ - 1} \\ \\ 3x + 3 = - 1 \\ \\ 3x = - 1 - 3 \\ \\ 3x = - 4 \\ \\ x = - \frac{ 4}{3}$

________//_______//_____

${7}^{3x - 6} = 49 \\ \\ {7}^{3x - 6} = {7}^{2} \\ \\ 3x - 6 = 2 \\ \\ 3x = 2 + 6 \\ \\ 3x = 8 \\ \\ x = \frac{8}{3}$

__________//_______//____

${9}^{7x + 3} = 729 \\ \\ {9}^{7x + 3} = {9}^{3} \\ \\ 7x + 3 = 3 \\ \\ 7x = 3 - 3 \\ \\ 7x = 0 \\ \\ x = \frac{0}{7} \\ \\ x = 0$

______//_______//______

${3}^{4x + 10} = \frac{1}{81} \\ \\ {3}^{4x + 10} = {3}^{4} \\ \\ 4x + 10 = 4 \\ \\ 4x = 4 - 10 \\ \\ 4x = - 6 \\ \\ x = \frac{ - 6 \div 2}{4 \div 2} \\ \\ x = - \frac{3}{2}$

Bons Estudos!