What is log_{10}((4x^3)/(y(x-2)^6)) ?

The solution to log_{10}((4x^3)/(y(x-2)^6)) is 2log_{10}(2)+3log_{10}(x)-log_{10}(y)-6log_{10}(x-2)

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simplify log_{10}((4x^3)/(y(x-2)^6))

simplify

lo g_{10} (\frac{4 x ^{3}}{y ( x - 2 ) ^{6}})

2 lo g_{10} (2) + 3 lo g_{10} (x) - lo g_{10} (y) - 6 lo g_{10} (x - 2)

Solution steps

lo g_{10} (\frac{4 x ^{3}}{y ( x - 2 ) ^{6}})

Apply log rule:

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

lo g_{10} (\frac{4 x ^{3}}{y ( x - 2 ) ^{6}}) = lo g_{10} (4 x^{3}) - lo g_{10} (y (x - 2)^{6})

= lo g_{10} (4 x^{3}) - lo g_{10} (y (x - 2)^{6})

Apply log rule:

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

lo g_{10} (4 x^{3}) = lo g_{10} (4) + lo g_{10} (x^{3}), lo g_{10} (y (x - 2)^{6}) = lo g_{10} (y) + lo g_{10} ((x - 2)^{6})

= lo g_{10} (4) + lo g_{10} (x^{3}) - (lo g_{10} ((x - 2)^{6}) + 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} (4) + 3 lo g_{10} (x) - (lo g_{10} (y) + lo g_{10} ((x - 2)^{6}))

Apply log rule:

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

lo g_{10} ((x - 2)^{6}) = 6 lo g_{10} (x - 2)

= lo g_{10} (4) + 3 lo g_{10} (x) - (lo g_{10} (y) + 6 lo g_{10} (x - 2))

lo g_{10} (4) = 2 lo g_{10} (2)

= 2 lo g_{10} (2) + 3 lo g_{10} (x) - (6 lo g_{10} (x - 2) + lo g_{10} (y))

- (lo g_{10} (y) + 6 lo g_{10} (x - 2)) : - lo g_{10} (y) - 6 lo g_{10} (x - 2)

= 2 lo g_{10} (2) + 3 lo g_{10} (x) - lo g_{10} (y) - 6 lo g_{10} (x - 2)

- lo g_{10} (8.4 \cdot 1 0^{- 10})

5 lo g_{m} (w) - \frac{1}{5} lo g_{m} (z) + 7 lo g_{m} (y)

\frac{( ( ln ( 1.1 ) - ln ( 0.9 ) ) )}{0.2}

lo g_{e} (\frac{5}{27})

- [\frac{1}{5} lo g_{2} (\frac{1}{5}) + \frac{4}{5} lo g_{2} (\frac{4}{5})]

What is log_{10}((4x^3)/(y(x-2)^6)) ?
The solution to log_{10}((4x^3)/(y(x-2)^6)) is 2log_{10}(2)+3log_{10}(x)-log_{10}(y)-6log_{10}(x-2)