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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} (3 x) = lo g_{10} (3) + lo g_{10} (x)

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

\frac{1}{- 0.20698} ln (\frac{28}{118})

\frac{1}{2} ln (\frac{x ^{2} + ( y - 1 ) ^{2}}{x ^{2}}) + ln (x)

2 ln (+ x^{3} ln (x))

ln (3 + 2 y) - ln (1 + 3 y)

2 ln (2) - 2 ln (3)

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