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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

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

lo g_{b} (b^{2}) = 2

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

lo g_{4} (\frac{y ^{8}}{16 x})

6 lo g_{5} (x) + 2 lo g_{5} (4 x) - \frac{1}{5} lo g_{5} (4 - x)

lo g_{x} (\frac{yz}{w})

- \frac{1}{3} ln (\frac{9}{19})

16.7 + 10 \cdot lo g_{10} (\frac{450}{70})

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