What is ln(((6x-4)(2y))/(3x)) ?

The solution to ln(((6x-4)(2y))/(3x)) is ln(6x-4)+ln(2)+ln(y)-ln(3)-ln(x)

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simplify ln(((6x-4)(2y))/(3x))

simplify

ln (\frac{( 6 x - 4 ) ( 2 y )}{3 x})

ln (6 x - 4) + ln (2) + ln (y) - ln (3) - ln (x)

Solution steps

ln (\frac{( 6 x - 4 ) ( 2 y )}{3 x})

Apply log rule:

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

ln (\frac{( 6 x - 4 ) ( 2 y )}{3 x}) = ln ((6 x - 4) (2 y)) - ln (3 x)

= ln (2 y (6 x - 4)) - ln (3 x)

Apply log rule:

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

ln ((6 x - 4) \cdot 2 y) = ln (6 x - 4) + ln (2) + ln (y), ln (3 x) = ln (3) + ln (x)

= ln (6 x - 4) + ln (2) + ln (y) - (ln (x) + ln (3))

- (ln (3) + ln (x)) : - ln (3) - ln (x)

= ln (6 x - 4) + ln (2) + ln (y) - ln (3) - ln (x)

lo g_{9} (4) - lo g_{9} (2) + 2 lo g_{9} (5)

lo g_{9} (4) - lo g_{9} (5)

lo g_{10} (\frac{x + 2}{x - 3})

4 lo g_{b} (x) - 6 lo g_{b} (y^{5})

ln (\frac{2 x ^{2} y}{z ^{4}})

What is ln(((6x-4)(2y))/(3x)) ?
The solution to ln(((6x-4)(2y))/(3x)) is ln(6x-4)+ln(2)+ln(y)-ln(3)-ln(x)