Question

Me ajudem com essa equação exponencial por favor​

Answer 1

Explicação passo-a-passo:

a)

$\bf{ {2}^{x + 4} = 16}$

$\bf{ {\cancel{2}}^{x + 4} = {\cancel{2}}^{4} }$

$\bf{x + 4 = 4}$

$\bf{x = + 4 - 4}$

$\pink{\boxed{ \bf{x = 0}}}$

b)

$\bf{ {5}^{2x + 1} = \frac{1}{625} }$

$\bf{ {\cancel{2}}^{2x + 1} = {\cancel{5}}^{ - 4} }$

$\bf{2x + 1 = - 4}$

$\bf{2x = - 4 - 1}$

$\bf{2x = - 5}$

$\pink{\boxed{ \bf{x = \frac{ - 5}{2} }}}$

ou

$\pink{\boxed{ \bf{x = - 2,5}}}$

c)

$\bf{ {729}^{2x} = 27 }$

$\bf{ { {(27}^{2} )}^{2x} = 27 }$

$\bf{ {27}^{4x} = 27 }$

$\bf{ {\cancel{27}}^{4x} = {\cancel{27}}^{1} }$

$\bf{4x = 1}$

$\pink{\boxed{ \bf{x = \frac{1}{4} }}}$

ou

$\pink{\boxed{ \bf{x = 0,25}}}$

d)

$\bf{ {2}^{ {x}^{2} - x} = 1}$

$\bf{ {\cancel{2}}^{ {x}^{2} - x } = {\cancel{2}}^{0} }$

$\bf{ {x}^{2} - x = 0 }$

$\bf{x \times (x - 1) = 0}$

$\bf{x = 0} \\ \bf{x - 1 = 0}$

$\bf{x = 0} \\ \bf{x = 1}$

$\pink{\boxed{ \bf{ x_{1} = 0 }}} \\ \pink{\boxed{ \bf{ x_{2} = 1 }}}$

e)

$\bf{ {5}^{ {x}^{2} - 9 } = 1}$

$\bf{ {\cancel{5}}^{ {x}^{2} - 9} = {\cancel{5}}^{0} }$

$\bf{ {x}^{2} - 9 = 0 }$

$\bf{ {x}^{2} = 9 }$

$\bf{x = \pm \sqrt{9} }$

$\bf{x = \pm3}$

$\bf{x = - 3} \\ \bf{x = 3}$

$\pink{\boxed{ \bf{ x_{1} = - 3}}} \\ \pink{\boxed{ \bf{ x_{2} = 3 }}}$

f)

$\bf{ {2}^{x - 4} = {8}^{x + 4} }$

$\bf{ {\cancel{2}}^{x - 4} = {\cancel{2}}^{3x + 12} }$

$\bf{x -4 = 3x + 12}$

$\bf{x - 3x - 4 = 12}$

$\bf{x - 3x = 12 + 4}$

$\bf{ - 2x = 16}$

$\bf{x = \frac{16}{ - 2} }$

$\pink{\boxed{ \bf{x = - 8}}}$

g)

$\bf{ {3}^{x + 2} = {81}^{2x + 2} }$

$\bf{ {\cancel{3}}^{x + 2} = {\cancel{3}}^{8x + 8} }$

$\bf{x + 2 = 8x + 8}$

$\bf{x - 8x = 8 - 2}$

$\bf{ - 7x = 6}$

$\pink{\boxed{ \bf{x = - \frac{6}{7} }}}$

ou

$\pink{\boxed{ \bf{x\approx - 0,85}}}$