What is log_{3}((sqrt(z))/9) ?

The solution to log_{3}((sqrt(z))/9) is log_{3}(sqrt(z))-2

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simplify log_{3}((sqrt(z))/9)

simplify

lo g_{3} (\frac{z}{9})

lo g_{3} (z) - 2

Solution steps

lo g_{3} (\frac{z}{9})

Apply log rule:

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

lo g_{3} (\frac{z}{9}) = lo g_{3} (z) - lo g_{3} (9)

= lo g_{3} (z) - lo g_{3} (9)

lo g_{3} (9) = 2

= lo g_{3} (z) - 2

lo g_{10} (\frac{x ^{9} y ^{5}}{z ^{3}})

ln (x - 1) - ln (x + 8)

lo g_{10} (x) - 4 lo g_{10} (y) + 7 lo g_{10} (z)

ln (1) - ln (7 e^{- x})

lo g_{5} (\frac{a ^{3}}{b ^{2}})

What is log_{3}((sqrt(z))/9) ?
The solution to log_{3}((sqrt(z))/9) is log_{3}(sqrt(z))-2