What is log_{10}((c^6)/(ab^3)) ?

The solution to log_{10}((c^6)/(ab^3)) is 6log_{10}(c)-log_{10}(a)-3log_{10}(b)

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simplify log_{10}((c^6)/(ab^3))

simplify

lo g_{10} (\frac{c ^{6}}{a b ^{3}})

6 lo g_{10} (c) - lo g_{10} (a) - 3 lo g_{10} (b)

Solution steps

lo g_{10} (\frac{c ^{6}}{a b ^{3}})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{10} (\frac{c ^{6}}{a b ^{3}}) = lo g_{10} (c^{6}) - lo g_{10} (a b^{3})

= lo g_{10} (c^{6}) - lo g_{10} (a b^{3})

lo g_{10} (c^{6}) = 6 lo g_{10} (c)

lo g_{10} (a b^{3}) = lo g_{10} (a) + 3 lo g_{10} (b)

= 6 lo g_{10} (c) - (lo g_{10} (a) + 3 lo g_{10} (b))

Apply the distributive law:

- (a + b) = - a - b

- (lo g_{10} (a) + 3 lo g_{10} (b)) = - lo g_{10} (a) - 3 lo g_{10} (b)

= 6 lo g_{10} (c) - lo g_{10} (a) - 3 lo g_{10} (b)

lo g_{b} (4) + lo g_{b} (3)

lo g_{6} (\frac{36 a ^{6} 1 - b}{c ( b + 5 ) ^{2}})

ln (\frac{17}{16})

lo g_{e} (9) + ln (8) - ln (10) - lo g_{e} (11)

lo g_{3} (\frac{x}{2}) + lo g_{3} (16) - lo g_{3} (4)

What is log_{10}((c^6)/(ab^3)) ?
The solution to log_{10}((c^6)/(ab^3)) is 6log_{10}(c)-log_{10}(a)-3log_{10}(b)