Question

Use logarithmic properties and solve for x

Answer 1

`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)`