If \( 6^{4 x-1}=6^{7} \), then \( \square=7 \)

To solve the equation \( 6^{4x-1} = 6^{7} \), we can use the property of exponents that states if the bases are the same, then the exponents must be equal. 1. Set the exponents equal to each other: \[ 4x - 1 = 7 \] 2. Solve for \( x \): - First, add 1 to both sides: \[ 4x = 7 + 1 \] \[ 4x = 8 \] - Next, divide both sides by 4: \[ x = \frac{8}{4} \] \[ x = 2 \] Thus, the value of \( x \) is \( 2 \). Now, according to your statement, \( \square = 7 \). However, the solution we found is \( x = 2 \). If you meant to find the value of \( 4x - 1 \) instead, we can substitute \( x = 2 \) back into the expression: \[ 4(2) - 1 = 8 - 1 = 7 \] So, indeed, \( \square = 7 \) is correct if \( \square \) represents \( 4x - 1 \). Final answer: \[ \boxed{7} \]