What is log_{3}((sqrt(x))/(27)) ?

The solution to log_{3}((sqrt(x))/(27)) is log_{3}(sqrt(x))-3

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simplify log_{3}((sqrt(x))/(27))

simplify

lo g_{3} (\frac{x}{27})

lo g_{3} (x) - 3

Solution steps

lo g_{3} (\frac{x}{27})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{3} (\frac{x}{27}) = lo g_{3} (x) - lo g_{3} (27)

= lo g_{3} (x) - lo g_{3} (27)

lo g_{3} (27) = 3

= lo g_{3} (x) - 3

lo g_{b} (x^{6} y)

\frac{1}{8} ln (x) + ln (y)

7 lo g_{2} (x) - \frac{1}{3} lo g_{2} (y)

lo g_{10} (2) + lo g_{10} (7)

lo g_{b} (\frac{x}{3})

What is log_{3}((sqrt(x))/(27)) ?
The solution to log_{3}((sqrt(x))/(27)) is log_{3}(sqrt(x))-3