What is log_{6}(2x)-log_{6}(x-3)3 ?

The solution to log_{6}(2x)-log_{6}(x-3)3 is log_{6}((2x)/((x-3)^3))

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simplify log_{6}(2x)-log_{6}(x-3)3

simplify

lo g_{6} (2 x) - lo g_{6} (x - 3) 3

lo g_{6} (\frac{2 x}{( x - 3 ) ^{3}})

Solution steps

lo g_{6} (2 x) - lo g_{6} (x - 3) \cdot 3

Apply log rule:

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

3 lo g_{6} (x - 3) = lo g_{6} ((x - 3)^{3})

= lo g_{6} (2 x) - lo g_{6} ((x - 3)^{3})

Apply log rule:

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

lo g_{6} (2 x) - lo g_{6} ((x - 3)^{3}) = lo g_{6} (\frac{2 x}{( x - 3 ) ^{3}})

= lo g_{6} (\frac{2 x}{( x - 3 ) ^{3}})

\frac{24}{π} ln (2 + 3)

- (- ln (x + 1) + ln (x - 1))

ln (\frac{0.001 \cdot 0.5}{0.5})

9 \cdot ln (4) - ln (2!) + 7 \cdot ln (2) - ln (7!) - 3 \cdot 4

0.75 \cdot ln (\frac{27}{11})

What is log_{6}(2x)-log_{6}(x-3)3 ?
The solution to log_{6}(2x)-log_{6}(x-3)3 is log_{6}((2x)/((x-3)^3))