Question

Resolva as seguintes equações:

a) log 4 2x =2

b) log 2 (log 3 x) =2

c) lag x + 1 (x² + 7) =2​

Answer 1

Resposta:

$log 4 2x =2\\\\2x=100\\\\x=\frac{50}{21}\\\\\\log 2 (log 3 x) =2\\\\\frac{\log _{10}\left(2\right)\log _{10}\left(3x\right)}{\log _{10}\left(2\right)}=\frac{2}{\log _{10}\left(2\right)}\\\\\log _{10}\left(3x\right)=\frac{2}{\log _{10}\left(2\right)}\\\\3x=10^{\frac{2}{\log _{10}\left(2\right)}}\\\\x=\frac{10^{\frac{2}{\log _{10}\left(2\right)}}}{3}\\\\\\\\ lag x + 1 (x^2 + 7) =2​\\\\x+x^2+7=2\\\\x+x^2+7-2=2-2\\\\x^2+x+5=0$

$x_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}\\\\x_1=\frac{-1+\sqrt{19}i}{2\cdot \:1}\\\\\:x_2=\frac{-1-\sqrt{19}i}{2\cdot \:1}\\\\x=-\frac{1}{2}+i\frac{\sqrt{19}}{2}\\\\\:x=-\frac{1}{2}-i\frac{\sqrt{19}}{2}$

Answer 2

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_4\:2x = 2}$

$\mathsf{2x = 4^2}$

$\mathsf{2x = 16}$

$\mathsf{x = \dfrac{16}{2}}$

$\boxed{\boxed{\mathsf{x = 8}}}\leftarrow\textsf{letra A}$

$\mathsf{log_2\:(log_3\:x) = 2}$

$\mathsf{log_3\:x = 2^2}$

$\mathsf{log_3\:x = 4}$

$\mathsf{x = 3^4}$

$\boxed{\boxed{\mathsf{x = 81}}}\leftarrow\textsf{letra B}$

$\mathsf{log_{(x + 1)} (x^2 + 7) = 2}$

$\mathsf{(x + 1)^2 = (x^2 + 7)}$

$\mathsf{x^2 + 2x + 1 = x^2 + 7}$

$\mathsf{2x + 1 = 7}$

$\mathsf{2x = 7 - 1}$

$\mathsf{2x = 6}$

$\mathsf{x = \dfrac{6}{2}}$

$\boxed{\boxed{\mathsf{x = 3}}}\leftarrow\textsf{letra C}$