SOLVE :- log tan (30 degrees) to the base 9 ???

Question

LOGARITHMS + TRIGONOMETRY

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Answer 1

The answer is -1 and this is why:

log tan (30 degrees) to the base 9 ???

tan (30degrees)=1/2 / (sqrt( 3))/2=1/sqrt(3)
Since
log(base b)(a)= ln a/ln b

log(base 9)(tan(30 deg))=
log(base9)(1/sqrt(3))=
=ln((3)^(-1/2))/ln(9)=
=(-1/2)(2)(Ln(3)/ln(3))=-1

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