Question

3 by 2 raise to the power x is equals to 81 upon 16

Answer 1

Answer:

$\left( \dfrac{ 3 }{ 2 } \right) ^x = \dfrac{ 8 1 }{ 1 6 }\quad : \quad x = 4$

Step-by-step explanation:

$\left( \dfrac{ 3 }{ 2 } \right) ^x = \dfrac{ 8 1 }{ 1 6 }$

$\gray{\mathrm{ C o n v e r t \: } \dfrac{ 8 1 }{ 1 6 } \mathrm{ \: t o \: b a s e \: } \left( \dfrac{ 3 }{ 2 } \right)}$

$\gray{ \dfrac{ 8 1 }{ 1 6 } = \left( \dfrac{ 3 }{ 2 } \right) ^4}$

$\left( \dfrac{ 3 }{ 2 } \right) ^x = \left( \dfrac{ 3 }{ 2 } \right) ^4$

$\gray{ \mathrm{ I f \: } a ^{ f \left( x \right) } = a ^{ g \left( x \right) }\mathrm{ , \: t h e n \: } f \left( x \right) = g \left( x \right)}$

$x = 4$