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

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

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

expand

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

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

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

Apply log rule:

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

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

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

- lo g_{10} (4.2 \cdot 1 0^{- 12})

5 ln (\frac{y}{x} + 1) - 4 ln (\frac{y}{x} + 2) + ln (x)

ln (9) - 3 ln (x) - 2 ln (y)

lo g_{10} (2) + 3 lo g_{10} (x) - \frac{1}{2} lo g_{10} (y)

ln (\frac{4.1 \cdot 1 0 ^{8}}{1.7 \cdot 1 0 ^{7}})

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