If log9x + log3x =3/2 then x is
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x = 3 if log₉x + log₃x =3/2
Step-by-step explanation:
log₉x + log₃x =3/2
as we know that logₐb = log b / log a
=> logx/ log 9 + log x / log 3 = 3/2
=> logx / log (3)² + log x / log 3 = 3/2
log aⁿ = n log a
=> logx /2 log (3) + log x / log 3 = 3/2
multiplying by 2 log (3) both sides
=> log x + 2 log x = 3 * log 3
=> 3 log x = 3 log 3
Dividing by 3 both sides
=> log x = log 3
=> x = 3
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