Question

Encontre o conjunto solução da equação exponencial ( √2 )^3x-1 = (^3 √16)^2x-1​

Answer 1

(√2 )^3x-1 = ( ³√16)^2x-1

2^(3x-1/2) = 16^(2x-1)/3

2^(3x-1/2) = 2^4(2x-1)/3

(3x-1/2) = 4(2x-1)/3

3.(3x-1) = 2.4(2x-1)

9x-3 = 16x-8

9x -16x = -8 +3

-7x = -5

x = 5/7 ✓

Answer 2

Resposta:

Equação exponencial:

${\color{blue}{(\sqrt{2})^{3x-1}=(\sqrt[3]{16})^{2x-1}}}$

$(2^{\frac{1}{2}})^{3x-1}=(16^{\frac{1}{3}})^{2x-1}$

$(2)^{\frac{3x-1}{2}}=(16)^{\frac{2x-1}{3}}$

$(2)^{\frac{3x-1}{2}}=(2^4)^{\frac{2x-1}{3}}$

$(\cancel{2})^{\frac{3x-1}{2}}=(\cancel{2})^{\frac{8x-4}{3}}$

$\frac{3x-1}{2}=\frac{8x-4}{3}$

$(3x-1).3=(8x-4).2$

$9x-3=16x-8$

$9x-16x=-8+3$

$-7x=-5\:\:/(-1)$

$7x=5$

$\boxed{\begin{array}{Ir}x=\frac{5}{7}\end{array}}$

Espero ter ajudado bastante!)