What is ln((5x+2)(3x-4)^2) ?

The solution to ln((5x+2)(3x-4)^2) is ln(5x+2)+2ln(3x-4)

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simplify ln((5x+2)(3x-4)^2)

simplify

ln ((5 x + 2) (3 x - 4)^{2})

ln (5 x + 2) + 2 ln (3 x - 4)

Solution steps

ln ((5 x + 2) (3 x - 4)^{2})

Apply log rule:

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

ln ((5 x + 2) (3 x - 4)^{2}) = ln (5 x + 2) + ln ((3 x - 4)^{2})

= ln (5 x + 2) + ln ((3 x - 4)^{2})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((3 x - 4)^{2}) = 2 ln (3 x - 4)

= ln (5 x + 2) + 2 ln (3 x - 4)

y^{^{''}} - 4 y^{^{'}} + 4 y = x^{2}

(x + 1)^{\frac{1}{2}}

y^{^{'}} = 6 x (y - 1)^{\frac{2}{3}}

k = 0 \sum \infty \frac{k}{2 ^{k}} x^{k}

y^{^{''}} + 214 y^{^{'}} + 14 y = 0

What is ln((5x+2)(3x-4)^2) ?
The solution to ln((5x+2)(3x-4)^2) is ln(5x+2)+2ln(3x-4)