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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

\frac{y ^{2}}{x ^{2}} + ln (\frac{x ^{6}}{y ^{2}})

\frac{ln ( 15 ) - ln ( 2 )}{ln ( 1.05 ) - ln ( 1.19 )}

\frac{ln ( 2 + \frac{( 5 i )}{( n )} ) \cdot ( 5 )}{( n )}

ln ((0.5 + \frac{0.044315}{2}) \cdot 1.05)

lo g_{8} (5) + \frac{1}{4} lo g_{8} (x)

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