Question

Se log3 3x - log9 x - log3 x =2 ,então log1/3 3x vale ?

Answer 1

log3(3x) - log9(x) - log3(x) = 2

log(3x)/log(3) - log(x)/log(9) - log(x)/log(3) = 2

log(3x) - log(x)/2 - log(x) = 2log(3)

2log(3x) - log(x) - 2log(x) = 4log(3)

2log(3x) - 3log(x) = log(81)

2log(3) + 2log(x) - 3log(x) = log(81)

-log(x) = log(81) - log(9)

log(x) = log(9) - log(81)

log(x) = log(9/81) = log(1/9)

x = 1/9

log1/3(3x) = log1/3(3/9) = log1/3(1/3) = 1