Question

Find the value of the expression log27√3

Answer 1

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

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

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

Answer 2

$\log_{27}\sqrt3=\dfrac{\log_3\sqrt3}{\log_327}=\dfrac{\dfrac{1}{2}}{3}= \dfrac{1}{6}$