Question

Resolva as seguintes equações exponenciais:​

Answer 1

$h)\\\\3^{x-5}~=~27^{1-x}\\\\\\3^{x-5}~=~\left(3^3\right)^{1-x}\\\\\\3^{x-5}~=~3^{3.(1-x)}\\\\\\3\!\!\!\backslash^{x-5}~=~3\!\!\!\backslash^{3.(1-x)}\\\\\\x-5~=~3.(1-x)\\\\\\x-5~=~3-3x\\\\\\x+3x~=~3+5\\\\\\4x~=~8\\\\\\x~=~\frac{8}{4}\\\\\\\boxed{x~=~2}$

$i)\\\\\left(\frac{2}{3}\right)^x~=~\left(\frac{8}{27}\right)\\\\\\\left(\frac{2}{3}\right)^x~=~\left(\frac{2^3}{3^3}\right)\\\\\\\left(\frac{2}{3}\!\!\!\backslash\right)^x~=~\left(\frac{2}{3}\right)^3\\\\\\\left(\frac{2}{3}\!\!\!\backslash\right)^x~=~\left(\frac{2}{3}\!\!\!\backslash\right)^3\\\\\\\boxed{x~=~3}$

$j)\\\\49^x~=~\sqrt{7}\\\\\\\left(7^2\right)^x~=~7^{\frac{1}{2}}\\\\\\7^{2\,.\,x}~=~7^{\frac{1}{2}}\\\\\\7\!\!\!\backslash^{2x}~=~7\!\!\!\backslash^{\frac{1}{2}}\\\\\\2x~=~\frac{1}{2}\\\\\\x~=~\frac{1}{2~.~2}\\\\\\\boxed{x~=~\frac{1}{4}}$