What is log_{6}(ab^3c^{-2}) ?

The solution to log_{6}(ab^3c^{-2}) is log_{6}(a)+3log_{6}(b)-2log_{6}(c)

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simplify log_{6}(ab^3c^{-2})

simplify

lo g_{6} (a b^{3} c^{- 2})

lo g_{6} (a) + 3 lo g_{6} (b) - 2 lo g_{6} (c)

Solution steps

lo g_{6} (a b^{3} c^{- 2})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{6} (a b^{3} c^{- 2}) = lo g_{6} (a) + lo g_{6} (b^{3}) + lo g_{6} (c^{- 2})

= lo g_{6} (a) + lo g_{6} (b^{3}) + lo g_{6} (c^{- 2})

lo g_{6} (b^{3}) = 3 lo g_{6} (b)

lo g_{6} (c^{- 2}) = - 2 lo g_{6} (c)

= lo g_{6} (a) + 3 lo g_{6} (b) - 2 lo g_{6} (c)

2 lo g_{2^{x}} (+ 4 lo g_{2^{y}} (- 6 lo g_{2^{z}} (x)))

ln (\frac{1.5 \cdot 1 0 ^{11}}{1 0 ^{- 3}})

2.34 + lo g_{10} (\frac{1 \cdot 1 0 ^{- 7}}{0.1})

ln (\frac{1}{1 0 ^{3}})

lo g_{10} (y^{9} x)

What is log_{6}(ab^3c^{-2}) ?
The solution to log_{6}(ab^3c^{-2}) is log_{6}(a)+3log_{6}(b)-2log_{6}(c)