What is 27log_{10}(x)+log_{10}(y)-12log_{10}(z) ?

The solution to 27log_{10}(x)+log_{10}(y)-12log_{10}(z) is log_{10}((x^{27}y)/(z^{12)})

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simplify 27log_{10}(x)+log_{10}(y)-12log_{10}(z)

simplify

27 lo g_{10} (x) + lo g_{10} (y) - 12 lo g_{10} (z)

lo g_{10} (\frac{x ^{27} y}{z ^{12}})

Solution steps

27 lo g_{10} (x) + lo g_{10} (y) - 12 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

27 lo g_{10} (x) = lo g_{10} (x^{27})

= lo g_{10} (x^{27}) + lo g_{10} (y) - 12 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{27}) + lo g_{10} (y) = lo g_{10} (x^{27} y)

= lo g_{10} (x^{27} y) - 12 lo g_{10} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

12 lo g_{10} (z) = lo g_{10} (z^{12})

= lo g_{10} (x^{27} y) - lo g_{10} (z^{12})

Apply log rule:

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

lo g_{10} (x^{27} y) - lo g_{10} (z^{12}) = lo g_{10} (\frac{x ^{27} y}{z ^{12}})

= lo g_{10} (\frac{x ^{27} y}{z ^{12}})

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What is 27log_{10}(x)+log_{10}(y)-12log_{10}(z) ?
The solution to 27log_{10}(x)+log_{10}(y)-12log_{10}(z) is log_{10}((x^{27}y)/(z^{12)})