Question

resolver a equação
3^(3x/2)=125^4

Answer 1

EAE mano,

usa a propriedade de log,

$\boxed{log_b(c)^n\Rightarrow n\cdot log_b(c)}$

$3^{ \tfrac{3x}{2} }=125^4\\ log(3)^{ \tfrac{3x}{2} }=log(5^3)^4\\ log(3)^{ \tfrac{3x}{2} }=log(5)^{12}\\ \dfrac{3}{2}x\cdot log(3)=12\cdot log(5)\\\\ log3=0,4771~~e~~log5=0,6990\\\\ \dfrac{3}{2}x\cdot0,4771=12\cdot0,6990\\\\ 0,7156x=8,3880\\\\ x= \dfrac{8,3880}{0,7156}\\\\ x=11,7216\\\\\\ \Large\boxed{\boxed{S=\{11,7216\}}}$

Tenha ótimos estudos ;D