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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

lo g_{10} ((2 x)^{3}) = 3 lo g_{10} (2 x)

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

Apply log rule:

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

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

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

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

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

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