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

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

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expand log_{10}((2x)/(y^3))

expand

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

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

Solution steps

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

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

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

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

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

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

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

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

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

ln (\frac{1}{x 2 π})

4 lo g_{2} (y - 3) - 6 lo g_{2} (y + 9)

ln (- \frac{2}{5} e^{10 t})

lo g_{e} (x^{2}) - lo g_{e} (lo g_{e} (x))

ln (\frac{e ^{x^{2}}}{x ^{2}})

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