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Question
Given: log3 m = x and log3 n = y.
If 2 log3 A = 5x - 3y; find A in terms of m and n.
Solution
Given that log3m = x and log3n = y
⇒ 3x = m and 3y = 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 ))`
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