Question

6) Calcule os exercícios abaixo

Answer 1

Resposta:

Solução:

a)

$\sf \displaystyle 729^{2x} = 27$

$\sf \displaystyle (3^6)^{2x} = 3^3$

$\sf \displaystyle \diagup\!\!\!{ 3}^{12x} = \diagup\!\!\!{ 3}^3$

$\sf \displaystyle 12x = 3$

$\sf \displaystyle x = \dfrac{3}{12}$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x = \dfrac{1}{4} }}} \quad \gets \mathbf{ Resposta }$

b)

$\sf \displaystyle (5^x)^{x -2} = 25^x$

$\sf \displaystyle (5)^{x^{2} -2x} = (5^2)^x$

$\sf \displaystyle \diagup\!\!\!{ 5}^{x^{2} -2x} = \diagup\!\!\!{5}^{2x}$

$\sf \displaystyle x^{2} -2x = 2x$

$\sf \displaystyle x^{2} -2x - 2x = 0$

$\sf \displaystyle x^{2} - 4x = 0$

$\sf \displaystyle x \cdot (x - 4) = 0$

$\boxed{ \boldsymbol{ \sf \displaystyle x' = 0 }} \quad \gets \mathbf{ Resposta }$

$\sf \displaystyle x - 4 = 0$

$\sf \displaystyle x = 0 + 4$

$\boxed{ \boldsymbol{ \sf \displaystyle x'' = 4 }} \quad \gets \mathbf{ Resposta }$

c)

$\sf \displaystyle 10^{2x - 1} - 10^x = 0$

$\sf \displaystyle \diagup\!\!\!{ 10}^{2x - 1} = \diagup\!\!\!{ 10}^x$

$\sf \displaystyle 2x - 1 = x$

$\sf \displaystyle 2x -x = 1$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x = 1 }}} \quad \gets \mathbf{ Resposta }$

d)

$\sf \displaystyle \left( \dfrac{1}{2} \right )^{x^2 -3} = 4$

$\sf \displaystyle \left( \dfrac{1}{2} \right )^{x^2 -3} = \left ( \dfrac{1}{4} \right )^{-\:1}$

$\sf \displaystyle \left( \dfrac{1}{2} \right )^{x^2 -3} = \left[ \left ( \dfrac{1}{2} \right )^2\right ]^{-\:1}$

$\sf \displaystyle \left( \dfrac{1}{2} \right )^{x^2 -3} = \left ( \dfrac{1}{2} \right )^{-\:2}$

$\sf \displaystyle x^{2} -3 = - 2$

$\sf \displaystyle x^{2} = - 2 + 3$

$\sf \displaystyle x^{2} = 1$

$\sf \displaystyle x = \pm\:\sqrt{1}$

$\sf \displaystyle x = \pm\: 1$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x' = -\;1 }}} \quad \gets \mathbf{ Resposta }$

$\boxed{ \boxed { \boldsymbol{ \sf \displaystyle x'' = 1 }}} \quad \gets \mathbf{ Resposta }$

Explicação passo-a-passo: