What is 2log_{6}(x-7)+log_{6}(9)-2 ?

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

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simplify 2log_{6}(x-7)+log_{6}(9)-2

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 lo g_{10} (3) - 3 lo g_{10} (x)

lo g_{b} (15) - 3 lo g_{b} (12)

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

ln (2 u) - ln (\frac{u}{2})

lo g_{a} (3 x yz)

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