\( (y-1)\log _{10}(4)=y\log _{10}(16)findy \)

Solve the equation \( (y-1)\log _{10}(4)=y\log _{10}(16) \). Solve the equation by following steps: - step0: Solve for \(y\): \(\left(y-1\right)\times \log_{10}{\left(4\right)}=y\log_{10}{\left(16\right)}\) - step1: Multiply the terms: \(\log_{10}{\left(4\right)}\times \left(y-1\right)=\log_{10}{\left(16\right)}\times y\) - step2: Expand the expression: \(2\log_{10}{\left(2\right)}\times y-2\log_{10}{\left(2\right)}=\log_{10}{\left(16\right)}\times y\) - step3: Move the variable to the left side: \(2\log_{10}{\left(2\right)}\times y-2\log_{10}{\left(2\right)}-\log_{10}{\left(16\right)}\times y=0\) - step4: Subtract the terms: \(-2\log_{10}{\left(2\right)}\times y-2\log_{10}{\left(2\right)}=0\) - step5: Move the constant to the right side: \(-2\log_{10}{\left(2\right)}\times y=0+2\log_{10}{\left(2\right)}\) - step6: Remove 0: \(-2\log_{10}{\left(2\right)}\times y=2\log_{10}{\left(2\right)}\) - step7: Change the signs: \(2\log_{10}{\left(2\right)}\times y=-2\log_{10}{\left(2\right)}\) - step8: Divide both sides: \(\frac{2\log_{10}{\left(2\right)}\times y}{2\log_{10}{\left(2\right)}}=\frac{-2\log_{10}{\left(2\right)}}{2\log_{10}{\left(2\right)}}\) - step9: Divide the numbers: \(y=-1\) The solution to the equation \( (y-1)\log _{10}(4)=y\log _{10}(16) \) is \( y=-1 \).