What is 7log_{6}(x-2)+2log_{6}(3x) ?

The solution to 7log_{6}(x-2)+2log_{6}(3x) is log_{6}(9x^2(x-2)^7)

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simplify 7log_{6}(x-2)+2log_{6}(3x)

simplify

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

lo g_{6} (9 x^{2} (x - 2)^{7})

Solution steps

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

Apply log rule:

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

7 lo g_{6} (x - 2) = lo g_{6} ((x - 2)^{7})

= lo g_{6} ((x - 2)^{7}) + 2 lo g_{6} (3 x)

Apply log rule:

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

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

= lo g_{6} ((x - 2)^{7}) + lo g_{6} ((3 x)^{2})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{6} ((x - 2)^{7}) + lo g_{6} ((3 x)^{2}) = lo g_{6} ((3 x)^{2} (x - 2)^{7})

= lo g_{6} ((x - 2)^{7} (3 x)^{2})

Simplify

(x - 2)^{7} (3 x)^{2} : 9 x^{2} (x - 2)^{7}

= lo g_{6} (9 x^{2} (x - 2)^{7})

lo g_{10} (0.0001) - lo g_{10} (0.1)

4 lo g_{10} (x) + 3 lo g_{10} (y)

ln (\frac{( d - r ) ^{2}}{r ^{2}})

\frac{1}{2} (lo g_{5} (s) + lo g_{5} (t))

- lo g_{10} (1.2 \cdot 1 0^{- 5})

What is 7log_{6}(x-2)+2log_{6}(3x) ?
The solution to 7log_{6}(x-2)+2log_{6}(3x) is log_{6}(9x^2(x-2)^7)