\( \frac{\text { Queston }}{7^{x+1}}+7^{x-1}=50 \)

It seems there was an issue with solving the equation directly. Let's break down the problem step by step. We have the equation: \[ \frac{\text{Queston}}{7^{x+1}} + 7^{x-1} = 50 \] ### Step 1: Simplify the Equation First, let's rewrite the equation for clarity. We can express \( 7^{x-1} \) in terms of \( 7^{x+1} \): \[ 7^{x-1} = \frac{7^{x+1}}{7^2} = \frac{7^{x+1}}{49} \] Now, substituting this back into the equation gives us: \[ \frac{\text{Queston}}{7^{x+1}} + \frac{7^{x+1}}{49} = 50 \] ### Step 2: Eliminate the Denominator To eliminate the fractions, we can multiply the entire equation by \( 7^{x+1} \cdot 49 \): \[ 49 \cdot \text{Queston} + (7^{x+1})^2 = 50 \cdot 49 \cdot 7^{x+1} \] ### Step 3: Rearranging the Equation This leads to a quadratic equation in terms of \( 7^{x+1} \): \[ (7^{x+1})^2 - 50 \cdot 49 \cdot 7^{x+1} + 49 \cdot \text{Queston} = 0 \] Let \( y = 7^{x+1} \). The equation becomes: \[ y^2 - 2450y + 49 \cdot \text{Queston} = 0 \] ### Step 4: Solve the Quadratic Equation We can use the quadratic formula to solve for \( y \): \[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] where \( a = 1 \), \( b = -2450 \), and \( c = 49 \cdot \text{Queston} \). ### Step 5: Substitute Back to Find \( x \) Once we find \( y \), we can substitute back to find \( x \) using: \[ x = \log_7(y) - 1 \] ### Conclusion To proceed, we need the value of "Queston" to complete the calculations. Please provide the value of "Queston" so we can continue solving for \( x \).