Question

3^a-3^b=1800 find maximum value of a+b

Answer 1

Step-by-step explanation:

=> 1/3^-a - 1/3^-b = 1800

=> (3^-b - 3^-a) /(3^-a * 3^-b) = 1800

=> (3^-b - 3^-a) /(3^-(a+b)) = 1800

=> (3^-a - 3^-b) *(3^(a+b)) = 1800

=> 3^(a+b) = 1800/(3^-a - 3^-b)

=> log(3^(a+b)) = log [ 1800/(3^-a - 3^-b) ]

=> (a+b) = log(1800/(3^-a - 3^-b)) / (log3)

=> (a+b) = 2.09 * log(1800/3^a - 3^b)