Question

2. What is the simplified form of log base 9 root3 root3 root3 ?​

Answer 1

Answer:

log9√3√3√3=7/16

it helps you

Answer 2

SOLUTION

TO SIMPLIFY

$\sf{ log_{9}( \sqrt{3} \times \sqrt{3} \times \sqrt{3} ) }$

EVALUATION

$\sf{ log_{9}( \sqrt{3} \times \sqrt{3} \times \sqrt{3} ) }$

$\sf{ = log_{9} \bigg( {(\sqrt{3})}^{3} \bigg) }$

$\displaystyle\sf{ = 3log_{9} \bigg( \sqrt{3} \bigg) }$

$\displaystyle\sf{ = 3 \: \frac{ log( \sqrt{3} ) }{ log(9) } }$

$\displaystyle\sf{ = 3 \: \frac{ log( {3}^{ \frac{1}{2} } ) }{ log( {3}^{2} ) } }$

$\displaystyle\sf{ = 3 \: \frac{ \frac{1}{2} \: log( {3} ) }{ 2log( {3} ) } }$

$\displaystyle\sf{ = \frac{3}{4} \: \frac{ \: log( {3} ) }{ log( {3} ) } }$

$\displaystyle\sf{ = \frac{3}{4} }$

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