What is ln(-α(x-θ)^2)-ln(2θ^2x) ?

The solution to ln(-α(x-θ)^2)-ln(2θ^2x) is ln(-(α(x-θ)^2)/(2xθ^2))

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simplify ln(-α(x-θ)^2)-ln(2θ^2x)

simplify

ln (- α (x - θ)^{2}) - ln (2 θ^{2} x)

ln (- \frac{α ( x - θ ) ^{2}}{2 x θ ^{2}})

Solution steps

ln (- α (x - θ)^{2}) - ln (2 θ^{2} x)

Apply log rule:

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

ln (- α (x - θ)^{2}) - ln (2 x θ^{2}) = ln (\frac{- α ( x - θ ) ^{2}}{2 x θ ^{2}})

= ln (\frac{- α ( x - θ ) ^{2}}{2 θ ^{2} x})

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= ln (- \frac{α ( x - θ ) ^{2}}{2 x θ ^{2}})

6 ln (x) + 3 ln (y)

ln (18) + ln (z)

lo g_{10} (\frac{x ^{3} y ^{2}}{z ^{5}})

lo g_{5} (\frac{e ^{x}}{x ^{\frac{1}{2}}})

2.5 \cdot ln (\frac{70}{50}) - 0.8

What is ln(-α(x-θ)^2)-ln(2θ^2x) ?
The solution to ln(-α(x-θ)^2)-ln(2θ^2x) is ln(-(α(x-θ)^2)/(2xθ^2))