What is log_{6}(72)-log_{6}(144)-log_{6}(18) ?

The solution to log_{6}(72)-log_{6}(144)-log_{6}(18) is -2

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simplify log_{6}(72)-log_{6}(144)-log_{6}(18)

simplify

lo g_{6} (72) - lo g_{6} (144) - lo g_{6} (18)

- 2

Solution steps

lo g_{6} (72) - lo g_{6} (144) - lo g_{6} (18)

Apply log rule:

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

lo g_{6} (72) - lo g_{6} (144) = lo g_{6} (\frac{72}{144})

= lo g_{6} (\frac{72}{144}) - lo g_{6} (18)

Apply log rule:

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

lo g_{6} (\frac{72}{144}) - lo g_{6} (18) = lo g_{6} (\frac{\frac{72}{144}}{18})

= lo g_{6} (\frac{\frac{72}{144}}{18})

\frac{\frac{72}{144}}{18} = 6^{- 2}

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

Apply log rule:

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

= - 2

(lo g_{b} (x) - lo g_{b} (y)) + 6 lo g_{b} (v)

\frac{1}{2} (3 ln (3) - ln (2))

5 lo g_{10} (4 x^{2})

5 lo g_{10} (x) - 2 lo g_{10} (x + 7)

lo g_{10} (\frac{x ^{2} y ^{2}}{z})

What is log_{6}(72)-log_{6}(144)-log_{6}(18) ?
The solution to log_{6}(72)-log_{6}(144)-log_{6}(18) is -2