Question

Find the value of the expression log27√3

Answer 1

`\log_(27)\sqrt3=(\log_3\sqrt3)/(\log_327)=((1)/(2))/(3)= (1)/(6)`

Answer 2

`\log _( 27 ){ \left( \sqrt { 3 } \right) } \\ \\ =\frac { \log _( 3 ){ \left( \sqrt { 3 } \right) } }{ \log _( 3 ){ \left( 27 \right) } }`


`\\ \\ =\frac { \log _( 3 ){ \left( { 3 }^{ \frac { 1 }{ 2 } } \right) } }{ 3 } \\ \\ =\frac { \frac { 1 }{ 2 } \log _( 3 ){ 3 } }{ 3 } \\ \\ =\frac { \frac { 1 }{ 2 } }{ 3 }`


`\\ \\ =\frac { 1 }{ 2 } \cdot \frac { 1 }{ 3 } \\ \\ =\frac { 1 }{ 6 }`