What is ln((θ^2(3-2θ))/(36)) ?

The solution to ln((θ^2(3-2θ))/(36)) is 2ln(θ)+ln(3-2θ)-2ln(6)

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simplify ln((θ^2(3-2θ))/(36))

simplify

ln (\frac{θ ^{2} ( 3 - 2 θ )}{36})

2 ln (θ) + ln (3 - 2 θ) - 2 ln (6)

Solution steps

ln (\frac{θ ^{2} ( 3 - 2 θ )}{36})

Apply log rule:

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

ln (\frac{θ ^{2} ( 3 - 2 θ )}{36}) = ln (θ^{2} (3 - 2 θ)) - ln (36)

= ln (θ^{2} (- 2 θ + 3)) - ln (36)

Apply log rule:

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

ln (θ^{2} (3 - 2 θ)) = ln (θ^{2}) + ln (3 - 2 θ)

= ln (θ^{2}) + ln (- 2 θ + 3) - ln (36)

Apply log rule:

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

ln (θ^{2}) = 2 ln (θ)

= 2 ln (θ) + ln (3 - 2 θ) - ln (36)

ln (36) = 2 ln (6)

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

ln (6 y)

6 lo g_{5} (x) - 36 lo g_{5} (y)

lo g_{4} (\frac{\frac{x}{z}}{w})

ln (24) - ln (8)

ln (\frac{2 x}{3})

What is ln((θ^2(3-2θ))/(36)) ?
The solution to ln((θ^2(3-2θ))/(36)) is 2ln(θ)+ln(3-2θ)-2ln(6)