What is the exact value of x in the equation 3^(x+2)=5^(7x)?

Answer 1

3^(x+2)=5^(7x)
(x+2) log3 = (7x) log5
xlog3 - 7x log5 = -log3
x(log3-7log5) = -log3
x = log3/(7log5-log3)

the log can be whatever base you like. Usually 10 or e

If you take logs base 3 or 5, then
x = 1/(7log₃5 - 1)
or
x = log₅3/(7-log₅3)