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

Sagot :

[tex]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 } }[/tex]

[tex]\\ \\ 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 }[/tex]

[tex]\\ \\ x=\log _{ 3 }{ \left( 9\cdot 2 \right) } \\ \\ x=\log _{ 3 }{ 9+\log _{ 3 }{ 2 } } \\ \\ x=2+\log _{ 3 }{ 2 } \\ \\ [/tex]
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