Question

3(2^x)=6^(x-1). leave the solution and how u did the problem. leave answer in simplest logarithmic form

Answer 1

`3\cdot { 2 }^( x )={ 6 }^( x-1 )\\ \\ 3\cdot { 2 }^( x )=\frac { { 6 }^( x ) }{ 6 } \\ \\ 18\cdot { 2 }^( x )={ 6 }^( x )\\ \\ 18=\frac { { 6 }^( x ) }{ { 2 }^( x ) }`


`\\ \\ 18=\frac { { \left( 3\cdot 2 \right) }^( x ) }{ { 2 }^( x ) } \\ \\ 18=\frac { { 3 }^( x ){ \cdot 2 }^( x ) }{ { 2 }^( x ) } \\ \\ { 3 }^( x )=18\\ \\ \log _( 3 ){ 18=x }`


`\\ \\ x=\log _( 3 ){ \left( 9\cdot 2 \right) } \\ \\ x=\log _( 3 ){ 9+\log _( 3 ){ 2 } } \\ \\ x=2+\log _( 3 ){ 2 } \\ \\`