Question

solve 3 to the power x = 5to the power x-2

Answer 1

$3^x=5^{x-2}\\ \\ \Rightarrow log (3^x)=log(5^{x-2})\\ \\ \Rightarrow x\ log(3)=(x-2)\ log(5)\\ \\ \Rightarrow x\ log(3)=x\ log(5) - 2\ log(5)\\ \\ \Rightarrow x\ log(3)-x\ log(5) =- 2\ log(5)\\ \\ \Rightarrow x\ log(5)-x\ log(3)= 2\ log(5)\\ \\ \Rightarrow x\ (log(5)-log(3))= 2\ log(5)\\ \\ \Rightarrow x= \frac{2\ log(5)}{log(5)-log(3)}\\ \\ \Rightarrow x=\boxed{6.3013}$