What is log_{b}((x^2y)/(b^3)) ?

The solution to log_{b}((x^2y)/(b^3)) is 2log_{b}(x)+log_{b}(y)-3

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simplify log_{b}((x^2y)/(b^3))

simplify

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

2 lo g_{b} (x) + lo g_{b} (y) - 3

Solution steps

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

Apply log rule:

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

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

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

lo g_{b} (x^{2} y) = 2 lo g_{b} (x) + lo g_{b} (y)

lo g_{b} (b^{3}) = 3

= 2 lo g_{b} (x) + lo g_{b} (y) - 3

16.7 + 10 \cdot lo g_{10} (\frac{750}{100})

lo g_{4} (\frac{5 x y}{2 x + y})

lo g_{10} (16 x^{2})

\frac{3}{41} ln (2 e)

4 lo g_{10} (3) - 1 lo g_{10} (x)

What is log_{b}((x^2y)/(b^3)) ?
The solution to log_{b}((x^2y)/(b^3)) is 2log_{b}(x)+log_{b}(y)-3