If f(x)=log3x, what if f(1/9)?

Answer 1

If your expression means:

f(x) = log ( 3 x )

then

f(1/3) = log ( 3 ∙ 1 / 9 ) = log ( 3 / 9 ) = log ( 1 / 3 ) = - log ( 3 )

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Remark:

log ( 1 ) = 0

log ( 1 / n ) = log ( 1 ) - log ( n ) = 0 - log n = - log ( n)

that's why

log ( 1 / 3 ) = - log ( 3 )
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Answer 2

My typo.

f(1/9) = log ( 3 ∙ 1 / 9 ) = log ( 3 / 9 ) = log ( 1 / 3 ) = - log ( 3 )

Answer 3

If you mean log base 3, f(x) = log_3(x), then
f(1/9) = -2, since 1/9 = 3^-2