Question

1. Desenvolva a expressão utilizando as propriedades operatórias dos logaritmos: (foto anexada)

2. Resolva a equação: log2 (3x - 1) - log4 (x + 1) = ½.​

Answer 1

$\sf log _2\left(3x-1\right)-log _4\left(x+1\right)=\dfrac{1}{2}\\\\\\\sf \left(3x-1\right)^2=2\left(x+1\right)\\\\\\\sf x=1\ll Verdadeiro\\\:x=-\dfrac{1}{9}\ll Falso\\\\\\\to \boxed{\sf x=1}$

$\tt Conta \ 2 \\\\obs: bem \ complicada \ kk \\\\\\\sf \displaystyle log\sqrt{\frac{x^3\sqrt{z}}{z^3}}\\\\\\\sf =log _{10}\left(\left(\frac{x^3\sqrt{z}}{z^3}\right)^{\frac{1}{2}}\right)\\\\\\\sf =\frac{1}{2}log _{10}\left(\frac{x^3\sqrt{z}}{z^3}\right)\\\\\\\sf =\frac{1\cdot log _{10}\left(\frac{x^3\sqrt{z}}{z^3}\right)}{2}\\\\\\\sf =\frac{log _{10}\left(\frac{x^3\sqrt{z}}{z^3}\right)}{2}\\\\\\\sf =\frac{log _{10}\left(x^3\sqrt{z}\right)-3log _{10}\left(z\right)}{2}$

$\sf \boxed{\sf =\frac{log _{10}\left(\frac{x^3}{z^{\frac{5}{2}}}\right)}{2}}\\\\\\\tt Terminei \ kk$