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

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

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

expand

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

lo g_{10} (3 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)

3 x = 3 x

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

ln (\frac{x}{0.085})

ln (\frac{0.5}{x})

ln (2) - ln (7) + ln (5)

\frac{3}{2} lo g_{10} (x + 4) - 3 lo g_{10} (x) - ln (6)

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