What is 3log_{5}(x-1)-log_{5}(3-6x) ?

The solution to 3log_{5}(x-1)-log_{5}(3-6x) is log_{5}(((x-1)^3)/(3-6x))

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simplify 3log_{5}(x-1)-log_{5}(3-6x)

simplify

3 lo g_{5} (x - 1) - lo g_{5} (3 - 6 x)

lo g_{5} (\frac{( x - 1 ) ^{3}}{3 - 6 x})

Solution steps

3 lo g_{5} (x - 1) - lo g_{5} (3 - 6 x)

Apply log rule:

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

3 lo g_{5} (x - 1) = lo g_{5} ((x - 1)^{3})

= lo g_{5} ((x - 1)^{3}) - lo g_{5} (- 6 x + 3)

Apply log rule:

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

lo g_{5} ((x - 1)^{3}) - lo g_{5} (3 - 6 x) = lo g_{5} (\frac{( x - 1 ) ^{3}}{- 6 x + 3})

= lo g_{5} (\frac{( x - 1 ) ^{3}}{3 - 6 x})

ln (x) + ln (x - 4) - 2 ln (x + 1)

\frac{1}{2} (lo g_{10} (b) - lo g_{10} (c))

lo g_{10} (5 bm)

6 ln (x + 7) - ln (x)

lo g_{10} (\frac{x y ^{8}}{z ^{5}})

What is 3log_{5}(x-1)-log_{5}(3-6x) ?
The solution to 3log_{5}(x-1)-log_{5}(3-6x) is log_{5}(((x-1)^3)/(3-6x))