Question

determine o conjunto solucao das seguintes equacoes exponenciais (1 tipo)

Answer 1

Explicação passo-a-passo:

a)

$9^{x}=\sqrt{27}\\\\(3^{2})^{x}=27^{\frac{1}{2} } \\\\3^{2x}=(3^{3}) ^{\frac{1}{2} }\\\\3^{2x}=3^{\frac{3}{2} }\\\\\text Igualando\ os\ expoentes:\\\\2x=\dfrac{3}{2}\\\\x= \dfrac{3}{4} \\\\\boxed{\boxed{S=\bigg\{\frac{3}{4}\bigg\} }}$

b)

$49^{2x+3}=343\\\\(7^{2} )^{2x+3}=7^{3} \\\\7^{4x+6}=7^{3} \\\\\text Igulando\ os\ expoentes:\\\\4x+6=3\\\\4x=3-6\\\\4x=-3\\\\x=\dfrac{-3}{4} \\\\\boxed{\boxed{S=\bigg\{\frac{-3}{4}\bigg\} }}$

c)

$2^{x+7}=\dfrac{1}{64} \\\\2^{x+7}=\dfrac{1}{2^{6} } \\\\2^{x+7}=2^{-6}\\\\\text Igualando\ os\ expoentes:\\\\x+7=-6\\\\x=-6-7\\\\x=-13\\\\\boxed{\boxed{S=\{-13\}}}$