Question

determine o valor de x:. a)(4/9)^x=81/16. b)5^x+2=125^x.

Answer 1

$\left( \dfrac{4}{9}\right)^x= \dfrac{81}{16}\\\\ \left( \dfrac{2^2}{3^2}\right)^x= \dfrac{3^4}{2^4}\\\\ \left( \dfrac{2}{3}\right)^{2x}= \dfrac{3}{2}^4\\\\ \left( \dfrac{2}{3}\right)^{2x}= \dfrac{2}{3}^{-4}\\\\ 2x=-4\\\\ x= -2$


$5^{x+2}=125^x\\ 5^x\cdot5^2=(5^3)^x\\ 5^2\cdot5^x=5^{3x}\\\\ \dfrac{5^{3x}}{5^x}=5^2\\\\ 5^{3x} :5^x=5^2\\ 5^{3x-x}=5^2\\ \not5^{2x}=\not5^2\\\\ 2x=2\\ x=1$