b) \( 5^{3 x-2}=25^{x-1} \)

To solve the equation \( 5^{3x - 2} = 25^{x - 1} \), we can rewrite \( 25 \) as \( 5^2 \). This gives us \( 25^{x - 1} = (5^2)^{x - 1} = 5^{2(x - 1)} = 5^{2x - 2} \). Now we have \( 5^{3x - 2} = 5^{2x - 2} \). Since the bases are the same, we can set the exponents equal to each other: \( 3x - 2 = 2x - 2 \) Now, solving for \( x \): \( 3x - 2x = -2 + 2 \) \( x = 0 \) So, the solution is \( x = 0 \). If you wanted to double-check your answer, you can substitute \( x = 0 \) back into the original equation to ensure both sides are equal!