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

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

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

expand

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln^{3} (\frac{1}{x})

- lo g_{10} (5.8 \cdot 1 0^{- 9})

\frac{1}{2} ln (2) - ln (3) + \frac{1}{2} ln (4)

- ln (\frac{2.5}{3}) \cdot 400

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

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