Use Power Rule: \(\log_{b}{{x}^{c}}=c\log_{b}{x}\).
\[aProve\log{{(\frac{11}{13})}^{2}}+\log{\frac{130}{77}}-\log{\frac{55}{91}}=\log{2}\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[aProve\log{\frac{{11}^{2}}{{13}^{2}}}+\log{\frac{130}{77}}-\log{\frac{55}{91}}=\log{2}\]
Simplify \({11}^{2}\) to \(121\).
\[aProve\log{\frac{121}{{13}^{2}}}+\log{\frac{130}{77}}-\log{\frac{55}{91}}=\log{2}\]
Simplify \({13}^{2}\) to \(169\).
\[aProve\log{\frac{121}{169}}+\log{\frac{130}{77}}-\log{\frac{55}{91}}=\log{2}\]
Regroup terms.
\[Pre(\log{\frac{121}{169}})aov+\log{\frac{130}{77}}-\log{\frac{55}{91}}=\log{2}\]
Use Product Rule: \(\log_{b}{(xy)}=\log_{b}{x}+\log_{b}{y}\).
\[\log{\frac{\frac{\frac{130}{77}}{55}}{91}}+Pre(\log{\frac{121}{169}})aov=\log{2}\]
Simplify \(\frac{\frac{\frac{130}{77}}{55}}{91}\) to \(\frac{130}{77\times 55\times 91}\).
\[\log{(\frac{130}{77\times 55\times 91})}+Pre(\log{\frac{121}{169}})aov=\log{2}\]
Simplify \(77\times 55\) to \(4235\).
\[\log{(\frac{130}{4235\times 91})}+Pre(\log{\frac{121}{169}})aov=\log{2}\]
Simplify \(4235\times 91\) to \(385385\).
\[\log{\frac{130}{385385}}+Pre(\log{\frac{121}{169}})aov=\log{2}\]
Simplify \(\frac{130}{385385}\) to \(\frac{2}{5929}\).
\[\log{\frac{2}{5929}}+Pre(\log{\frac{121}{169}})aov=\log{2}\]
Subtract \(\log{\frac{2}{5929}}\) from both sides.
\[Pre(\log{\frac{121}{169}})aov=\log{2}-\log{\frac{2}{5929}}\]
Use Quotient Rule: \(\log_{b}{\frac{x}{y}}=\log_{b}{x}-\log_{b}{y}\).
\[Pre(\log{\frac{121}{169}})aov=\log{\frac{\frac{2}{2}}{5929}}\]
Cancel \(2\).
\[Pre(\log{\frac{121}{169}})aov=\log{\frac{1}{5929}}\]
Divide both sides by \(Pr\).
\[e(\log{\frac{121}{169}})aov=\frac{\log{\frac{1}{5929}}}{Pr}\]
Divide both sides by \(e\).
\[(\log{\frac{121}{169}})aov=\frac{\frac{\log{\frac{1}{5929}}}{Pr}}{e}\]
Simplify \(\frac{\frac{\log{\frac{1}{5929}}}{Pr}}{e}\) to \(\frac{\log{\frac{1}{5929}}}{Pre}\).
\[(\log{\frac{121}{169}})aov=\frac{\log{\frac{1}{5929}}}{Pre}\]
Divide both sides by \(\log{\frac{121}{169}}\).
\[aov=\frac{\frac{\log{\frac{1}{5929}}}{Pre}}{\log{\frac{121}{169}}}\]
Simplify \(\frac{\frac{\log{\frac{1}{5929}}}{Pre}}{\log{\frac{121}{169}}}\) to \(\frac{\log{\frac{1}{5929}}}{Pre\log{\frac{121}{169}}}\).
\[aov=\frac{\log{\frac{1}{5929}}}{Pre\log{\frac{121}{169}}}\]
Divide both sides by \(o\).
\[av=\frac{\frac{\log{\frac{1}{5929}}}{Pre\log{\frac{121}{169}}}}{o}\]
Simplify \(\frac{\frac{\log{\frac{1}{5929}}}{Pre\log{\frac{121}{169}}}}{o}\) to \(\frac{\log{\frac{1}{5929}}}{Pre(\log{\frac{121}{169}})o}\).
\[av=\frac{\log{\frac{1}{5929}}}{Pre(\log{\frac{121}{169}})o}\]
Divide both sides by \(v\).
\[a=\frac{\frac{\log{\frac{1}{5929}}}{Pre(\log{\frac{121}{169}})o}}{v}\]
Use Power Rule: \(\log_{b}{{x}^{c}}=c\log_{b}{x}\)\(\log{\frac{1}{5929}}\) -> \(\log{({5929}^{-1})}\) -> \(-\log{5929}\).
\[a=\frac{\frac{-\log{5929}}{Pre(\log{\frac{121}{169}})o}}{v}\]
Use Power Rule: \(\log_{b}{{x}^{c}}=c\log_{b}{x}\)\(\log{5929}\) -> \(\log{{77}^{2}}\) -> \(2\log{77}\).
\[a=\frac{\frac{-2\log{77}}{Pre(\log{\frac{121}{169}})o}}{v}\]
Move the negative sign to the left.
\[a=\frac{-\frac{2\log{77}}{Pre(\log{\frac{121}{169}})o}}{v}\]
Move the negative sign to the left.
\[a=-\frac{\frac{2\log{77}}{Pre(\log{\frac{121}{169}})o}}{v}\]
Simplify \(\frac{\frac{2\log{77}}{Pre(\log{\frac{121}{169}})o}}{v}\) to \(\frac{2\log{77}}{Pre(\log{\frac{121}{169}})ov}\).
\[a=-\frac{2\log{77}}{Pre(\log{\frac{121}{169}})ov}\]
a=-(2*log(77))/(Pr*e*log(121/169)*o*v)
