What is ln(C/((b^2+(x-a)^2)^2)) ?

The solution to ln(C/((b^2+(x-a)^2)^2)) is ln(C)-2ln(b^2+(x-a)^2)

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simplify ln(C/((b^2+(x-a)^2)^2))

simplify

ln \frac{C}{( b ^{2} + ( x - a ) ^{2} ) ^{2}}

ln (C) - 2 ln (b^{2} + (x - a)^{2})

Solution steps

ln \frac{C}{( b ^{2} + ( x - a ) ^{2} ) ^{2}}

Apply log rule:

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

ln \frac{C}{( b ^{2} + ( x - a ) ^{2} ) ^{2}} = ln (C) - ln ((b^{2} + (x - a)^{2})^{2})

= ln (C) - ln ((b^{2} + (x - a)^{2})^{2})

Apply log rule:

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

ln ((b^{2} + (x - a)^{2})^{2}) = 2 ln (b^{2} + (x - a)^{2})

= ln (C) - 2 ln (b^{2} + (x - a)^{2})

4 lo g_{10} (2) + lo g_{10}^{2} (5)

- lo g_{10} (6 \cdot 1 0^{- 10})

\frac{1}{2} ln (5 x^{2}) - \frac{1}{2} ln (2 x^{2})

- 6 (ln (3) - ln (2)) + \frac{7}{2} - 6 ln (2) + \frac{15}{2}

1.6 ln (\frac{2.242}{1.2})

What is ln(C/((b^2+(x-a)^2)^2)) ?
The solution to ln(C/((b^2+(x-a)^2)^2)) is ln(C)-2ln(b^2+(x-a)^2)