Solve. Simplify your answer. \( 7 \log _{13} x=14 \) \( x=\square \) Submit

Solve the equation \( 7 \log_{13}(x)=14 \). Solve the equation by following steps: - step0: Solve for \(x\): \(7\log_{13}{\left(x\right)}=14\) - step1: Find the domain: \(7\log_{13}{\left(x\right)}=14,x>0\) - step2: Divide both sides: \(\frac{7\log_{13}{\left(x\right)}}{7}=\frac{14}{7}\) - step3: Divide the numbers: \(\log_{13}{\left(x\right)}=2\) - step4: Convert the logarithm into exponential form: \(x=13^{2}\) - step5: Evaluate the power: \(x=169\) - step6: Check if the solution is in the defined range: \(x=169,x>0\) - step7: Find the intersection: \(x=169\) The solution to the equation \(7 \log_{13} x = 14\) is \(x = 169\).