Use logarithmic properties and solve for x

asked Dec 24, 2023 25.2k views

1 vote

by ABD

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1 vote

Answer:

x = 45 √(5)

Explanation:

${3}^{2 log_(3)(x) + log_(3)(5) } = {3}^{ 4log_(3)(15) }$

${3}^{ log_(3)( {x}^(2) ) } {3}^{ log_(3)(5) } = {3}^{ log_(3)( {15}^(4) ) }$

$5 {x}^(2) = {15}^(4)$

${x}^(2) = \frac{ {15}^(4) }{5}$

$x = \frac{ {15}^(2) }{ √(5) } ( ( √(5) )/( √(5) ) )$

$x = \frac{ {15}^(2) √(5) }{5} = 45 √(5)$

SureshAtt answered Dec 31, 2023

3.2k points

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