Question

Help on logarithmic equation

Answer 1

$\log _{ 2 }{ \left( 3-x \right) } +\log _{ 2 }{ 5 } =2\log _{ 3 }{ 5 } \\ \\ \log _{ 2 }{ \left( 5\left( 3-x \right) \right) } =\log _{ 3 }{ \left( { 5 }^{ 2 } \right) } \\ \\ { 2 }^{ \log _{ 3 }{ 25 } }=5\left( 3-x \right) \\ \\ { 2 }^{ \log _{ 3 }{ 25 } }=15-5x\\ \\ 5x=15-{ 2 }^{ \log _{ 3 }{ 25 } }\\ \\ x=\frac { 15 }{ 5 } -\frac { { 2 }^{ \log _{ 3 }{ 25 } } }{ 5 } \\ \\ x=3-\frac { { 2 }^{ \log _{ 3 }{ 25 } } }{ 5 }$