Question

(81)^x=3√3=1/(243)y, find the value of 8x+3y​

Answer 1

${81}^{x} = 3 \sqrt{3}$

${ ({3}^{4}) }^{x} = 3 \times {3}^{ \frac{1}{2} }$

${3}^{4x} = {3}^{1 + \frac{1}{2} }$

${3}^{4x} = {3}^{ \frac{3}{2} }$

$4x = \frac{3}{2}$

$x = \frac{3}{8}$

Now

$3 \sqrt{3} = \frac{1}{ {(243)}^{ y } }$

$3 \times {3}^{ \frac{1}{2} } = \frac{1}{ {(3)}^{5y} }$

${3}^{ \frac{3}{2} } = {3}^{ - 5y}$

$\frac{3}{2} = - 5y$

$y = \frac{ - 3}{10}$

Now

$8x + 3y$

$8( \frac{3}{8} ) + 3( \frac{ - 3}{10} )$

$3 + \frac{ - 9}{10}$

$\frac{30 - 9}{10}$

$= \frac{21}{10}$