Question

Given: log₃ m = x and log₃ n = y.
If 2 log₃ A = 5x - 3y; find A in terms of m and n.

Answer 1

Given that log₃m = x and log₃n = y
⇒ 3^x = m and 3^y = n 

Consider the given expression :
2log₃A = 5x - 3y
⇒ 2log₃A = 5 log₃m - 3log₃n

⇒ log₃A² = log₃m⁵ - log₃n³

⇒ log₃A² = `log_3( m^5/ n^3 )`

⇒ A² = `( m^5/ n^3 )`

⇒ A = `sqrt(( m^5/n^3 ))`