What is 28log_{10}(x)+log_{10}(y)-27log_{10}(z) ?

The solution to 28log_{10}(x)+log_{10}(y)-27log_{10}(z) is log_{10}((x^{28}y)/(z^{27)})

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simplify 28log_{10}(x)+log_{10}(y)-27log_{10}(z)

simplify

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

lo g_{10} (\frac{x ^{28} y}{z ^{27}})

Solution steps

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

Apply log rule:

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

28 lo g_{10} (x) = lo g_{10} (x^{28})

= lo g_{10} (x^{28}) + lo g_{10} (y) - 27 lo g_{10} (z)

Apply log rule:

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

lo g_{10} (x^{28}) + lo g_{10} (y) = lo g_{10} (x^{28} y)

= lo g_{10} (x^{28} y) - 27 lo g_{10} (z)

Apply log rule:

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

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

= lo g_{10} (x^{28} y) - lo g_{10} (z^{27})

Apply log rule:

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

lo g_{10} (x^{28} y) - lo g_{10} (z^{27}) = lo g_{10} (\frac{x ^{28} y}{z ^{27}})

= lo g_{10} (\frac{x ^{28} y}{z ^{27}})

10 lo g_{10} (\frac{320 \cdot 1 0 ^{- 7}}{1 0 ^{- 12}})

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

lo g_{a} (5 a x a^{4} x^{3} a)

ln ((8^{x} (3 x^{3} + 6)^{2})^{8} (9 x^{4} - 1)^{2})

10 ln (\frac{50}{1 0 ^{- 12}})

What is 28log_{10}(x)+log_{10}(y)-27log_{10}(z) ?
The solution to 28log_{10}(x)+log_{10}(y)-27log_{10}(z) is log_{10}((x^{28}y)/(z^{27)})