Question

DETERMINE O VALOR DE X NAS EQUAÇÕES ABAIXO:​

Answer 1

$\boxed{\begin{array}{l}\tt a)~\sf 2^x=32\\\begin{array}{c|c}\sf32&\sf2\\\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\\\sf 32=2^5\\\sf 2^x=2^5\\\sf x=5\end{array}}$

$\boxed{\begin{array}{l}\tt b)~\sf 5^x=125\\\begin{array}{c|c}\sf125&\sf5\\\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 125=5^3\\\sf5^x=5^3\\\sf x=5\end{array}}$

$\boxed{\begin{array}{l}\tt c)~\sf 9^x=27\\\begin{array}{c|c}\sf27&\sf3\\\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 27=3^3~~~9=3^2\\\sf (3^2)^x=3^3\\\sf 3^{2x}=3^3\\\sf 2x=3\\\sf x=\dfrac{3}{2}\end{array}}$

$\boxed{\begin{array}{l}\tt d)~\sf2^x=\dfrac{1}{16}\\\begin{array}{c|c}\sf16&\sf2\\\sf8&\sf2\\\sf4&\sf2\\\sf2&\sf2\\\sf1\end{array}\\\sf 16=2^4\\\sf\dfrac{1}{16}=\bigg(\dfrac{1}{2}\bigg)^4=2^{-4}\\\sf 2^x=2^{-4}\\\sf x=-4\end{array}}$

$\boxed{\begin{array}{l}\tt e)~\sf\bigg(\dfrac{1}{3}\bigg)^x=9\\\begin{array}{c|c}\sf9&\sf3\\\sf3&\sf3\\\sf1\end{array}\\\sf 9=3^2=\bigg(\dfrac{1}{3}\bigg)^{-2}\\\sf \bigg(\dfrac{1}{3}\bigg)^x=\bigg(\dfrac{1}{3}\bigg)^{-2}\\\sf x=-2\end{array}}$

$\boxed{\begin{array}{l}\tt f)~\sf 7^x=\sqrt{7}\\\sf 7^x=7^{\frac{1}{2}}\\\sf x=\dfrac{1}{2}\end{array}}$

$\boxed{\begin{array}{l}\tt g)~\sf0,25^x=2\\\sf0,25=\dfrac{25\div25}{100\div25}=\dfrac{1}{4}=\bigg(\dfrac{1}{2}\bigg)^2=2^{-2}\\\sf (2^{-2})^x=2\\\sf 2^{-2x}=2^1\\\sf -2x=1\cdot(-1)\\\sf 2x=-1\\\sf x=-\dfrac{1}{2}\end{array}}$

$\boxed{\begin{array}{l}\tt h)~\sf 25^x=\sqrt[\sf3]{\sf5}\\\begin{array}{c|c}\sf25&\sf5\\\sf5&\sf5\\\sf1\end{array}\\\sf 25=5^2\\\sf(5^2)^{x}=5^{\frac{1}{3}}\\\sf 5^{2x}=5^{\frac{1}{3}}\\\sf 2x=\dfrac{1}{3}\\\\\sf 6x=1\\\sf x=\dfrac{1}{6}\end{array}}$