What is log_{3}((ab^2)/3) ?

The solution to log_{3}((ab^2)/3) is log_{3}(a)+2log_{3}(b)-1

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simplify log_{3}((ab^2)/3)

simplify

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

lo g_{3} (a) + 2 lo g_{3} (b) - 1

Solution steps

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

Apply log rule:

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

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

= lo g_{3} (a b^{2}) - lo g_{3} (3)

lo g_{3} (a b^{2}) = lo g_{3} (a) + 2 lo g_{3} (b)

lo g_{3} (3) = 1

= lo g_{3} (a) + 2 lo g_{3} (b) - 1

lo g_{3} (8 x)

ln (\frac{x}{5})

3 ln (y) + 5 ln (z)

lo g_{b} (\frac{x ^{2}}{z ^{5} y})

4 lo g_{3} (x^{2}) - 3 lo g_{3} (x^{3})

What is log_{3}((ab^2)/3) ?
The solution to log_{3}((ab^2)/3) is log_{3}(a)+2log_{3}(b)-1