Question

5^3x-1 = ($\frac{1}{25}$)^2x+3

Answer 1

$5^{3x-1}=\left(\dfrac{1}{25}\right)^{2x+3}\\ \\ \\ 5^{3x-1}=\ \left(\dfrac{1}{5^{2}}\right)^{2x+3}\\ \\ \\ 5^{3x-1}=\ \left(5^{-2}\right)^{2x+3}\\ \\ 5^{3x-1}=\ 5^{-2\cdot \left(2x+3\right)}\\ \\ 5^{3x-1}=\ 5^{-4x-6}\\ \\ 3x-1= -4x-6\\ \\ 3x+4x=-6+1\ \Rightarrow\ 7x=-5\ \Rightarrow\ x=\dfrac{-5}{7}$