Question

Resolva as equações exponenciais:​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{3^{14x - 2} = 19683^{2x + 1}}$

$\mathsf{3^{14x - 2} = (3^9)^{2x + 1}}$

$\mathsf{3^{14x - 2} = 3^{18x + 9}}$

$\mathsf{14x - 2 = 18x + 9}$

$\mathsf{18x - 14x = -2 - 9}$

$\mathsf{4x = -11}$

$\boxed{\boxed{\mathsf{x = -\dfrac{11}{4}}}}$

$\mathsf{2^x - 192.2^x + 8192 = 0}$

$\mathsf{2^x(1 - 192) + 8192 = 0}$

$\mathsf{2^x(1 - 192) = -8192}$

$\mathsf{2^x = \dfrac{-8192}{-191}}$

$\mathsf{log\:2^x = log\:\dfrac{8192}{191}}$

$\mathsf{x\:log\:2 = log\:\dfrac{8192}{191}}$

$\mathsf{x = log\:\dfrac{8192}{191} \div log\:2}$

$\boxed{\boxed{\mathsf{x \approx 5,42}}}$