What is log_{10}((2x^2)/((y-1)^3)) ?

The solution to log_{10}((2x^2)/((y-1)^3)) is log_{10}(2)+2log_{10}(x)-3log_{10}(y-1)

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simplify log_{10}((2x^2)/((y-1)^3))

simplify

lo g_{10} (\frac{2 x ^{2}}{( y - 1 ) ^{3}})

lo g_{10} (2) + 2 lo g_{10} (x) - 3 lo g_{10} (y - 1)

Solution steps

lo g_{10} (\frac{2 x ^{2}}{( y - 1 ) ^{3}})

Apply log rule:

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

lo g_{10} (\frac{2 x ^{2}}{( y - 1 ) ^{3}}) = lo g_{10} (2 x^{2}) - lo g_{10} ((y - 1)^{3})

= lo g_{10} (2 x^{2}) - lo g_{10} ((y - 1)^{3})

lo g_{10} (2 x^{2}) = lo g_{10} (2) + 2 lo g_{10} (x)

lo g_{10} ((y - 1)^{3}) = 3 lo g_{10} (y - 1)

= lo g_{10} (2) + 2 lo g_{10} (x) - 3 lo g_{10} (y - 1)

\frac{1}{50} ln (\frac{1260}{980})

ln (8 e^{8 x})

2 (lo g_{10} (x + 1) - lo g_{10} (x - 4))

- (\frac{3}{11}) lo g_{2} (\frac{3}{11}) - (\frac{8}{11}) lo g_{2} (\frac{8}{11})

ln (\frac{2 ^{4}}{3 ^{4} 5 ^{3}})

What is log_{10}((2x^2)/((y-1)^3)) ?
The solution to log_{10}((2x^2)/((y-1)^3)) is log_{10}(2)+2log_{10}(x)-3log_{10}(y-1)