What is 3log_{a}(2x+1)-2log_{a}(2x-1) ?

The solution to 3log_{a}(2x+1)-2log_{a}(2x-1) is log_{a}(((2x+1)^3)/((2x-1)^2))

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simplify 3log_{a}(2x+1)-2log_{a}(2x-1)

simplify

3 lo g_{a} (2 x + 1) - 2 lo g_{a} (2 x - 1)

lo g_{a} (\frac{( 2 x + 1 ) ^{3}}{( 2 x - 1 ) ^{2}})

Solution steps

3 lo g_{a} (2 x + 1) - 2 lo g_{a} (2 x - 1)

Apply log rule:

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

3 lo g_{a} (2 x + 1) = lo g_{a} ((2 x + 1)^{3})

= lo g_{a} ((2 x + 1)^{3}) - 2 lo g_{a} (2 x - 1)

Apply log rule:

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

2 lo g_{a} (2 x - 1) = lo g_{a} ((2 x - 1)^{2})

= lo g_{a} ((2 x + 1)^{3}) - lo g_{a} ((2 x - 1)^{2})

Apply log rule:

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

lo g_{a} ((2 x + 1)^{3}) - lo g_{a} ((2 x - 1)^{2}) = lo g_{a} (\frac{( 2 x + 1 ) ^{3}}{( 2 x - 1 ) ^{2}})

= lo g_{a} (\frac{( 2 x + 1 ) ^{3}}{( 2 x - 1 ) ^{2}})

5 lo g_{10} (x) + 6 lo g_{10} (y)

ln (6) - ln (3) + ln (2 x)

lo g_{3} (\frac{3 a}{b c})

5 ln (x) + \frac{1}{2} ln (y)

What is 3log_{a}(2x+1)-2log_{a}(2x-1) ?
The solution to 3log_{a}(2x+1)-2log_{a}(2x-1) is log_{a}(((2x+1)^3)/((2x-1)^2))