25) \( 15^{-6 p-6}-6.2=62 \)

Solve the equation \( 15^{-6p-6}-6.2=62 \). Solve the equation by following steps: - step0: Solve for \(p\): \(15^{-6p-6}-6.2=62\) - step1: Move the constant to the right side: \(15^{-6p-6}=62+6.2\) - step2: Add the numbers: \(15^{-6p-6}=68.2\) - step3: Rewrite the expression: \(15^{-6p-6}=\frac{341}{5}\) - step4: Take the logarithm of both sides: \(\log_{15}{\left(15^{-6p-6}\right)}=\log_{15}{\left(\frac{341}{5}\right)}\) - step5: Evaluate the logarithm: \(-6p-6=\log_{15}{\left(\frac{341}{5}\right)}\) - step6: Move the constant to the right side: \(-6p=\log_{15}{\left(\frac{341}{5}\right)}+6\) - step7: Change the signs: \(6p=-\log_{15}{\left(\frac{341}{5}\right)}-6\) - step8: Divide both sides: \(\frac{6p}{6}=\frac{-\log_{15}{\left(\frac{341}{5}\right)}-6}{6}\) - step9: Divide the numbers: \(p=-\frac{\log_{15}{\left(\frac{341}{5}\right)}+6}{6}\) - step10: Simplify: \(p=\frac{-\log_{15}{\left(341\right)}+\log_{15}{\left(5\right)}-6}{6}\) - step11: Simplify: \(p=\frac{\log_{15}{\left(\frac{5}{341}\right)}-6}{6}\) - step12: Evaluate: \(p=\frac{\log_{15}{\left(5\right)}-\log_{15}{\left(341\right)}-6}{6}\) The solution to the equation \(15^{-6p-6}-6.2=62\) is \(p=\frac{\log_{15}(5)-\log_{15}(341)-6}{6}\).