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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2 ln (x) - 3 ln (y) + 5 ln (z)

lo g_{3} (x^{2} + 9 x + 18) - lo g_{3} (x + 3)

\frac{2}{3} lo g_{10} (\frac{5.96 x ^{1016}}{1 0 ^{4.4}})

lo g_{2} (\frac{x}{500})

ln (\frac{e ^{7}}{9})

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