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

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

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

simplify

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

ln (3 x - 1) - ln (2 x + 2)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (3 x - 1) - lo g_{e} (2 x + 2)

Apply log rule:

lo g_{e} (x) = ln (x)

= ln (3 x - 1) - ln (2 x + 2)

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

2 lo g_{c} (w) - \frac{1}{2} lo g_{c} (z) + 7 lo g_{c} (x)

ln ((\frac{3 y ^{3} - 3}{x ^{3}})^{- \frac{2}{9}}) - ln (x)

lo g_{10} (\frac{4}{5 x})

3 ln (2) + 2 ln (x) - \frac{1}{2} ln (x - 4)

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