Question 153867
Express the given quantity as a single logarithm. 
  ln(1+x^9)+ 1/2 ln(x)-ln(sin(x))

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ln(1+x^2) + ln(x^1/2) - ln(sin(x))

= ln[(1+x^2)(x)^(1/2) /sin(x)]

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Cheers,
Stan H.