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 }`