What is ln(205/200)+(1/2*0.02^2-0.05)*0.25 ?

The solution to ln(205/200)+(1/2*0.02^2-0.05)*0.25 is ln(205)-ln(200)+0.25((0.0004)/2-0.05)

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simplify ln(205/200)+(1/20.02^2-0.05)0.25

simplify

ln (\frac{205}{200}) + (\frac{1}{2} \cdot 0.0 2^{2} - 0.05) \cdot 0.25

ln (205) - ln (200) + 0.25 (\frac{0.0004}{2} - 0.05)

Decimal Notation

0.01224 \dots

Solution steps

ln (\frac{205}{200}) + (\frac{1}{2} \cdot 0.0 2^{2} - 0.05) \cdot 0.25

Apply log rule:

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

ln (\frac{205}{200}) = ln (205) - ln (200)

= ln (205) - ln (200) + 0.25 (0.0 2^{2} \cdot \frac{1}{2} - 0.05)

\frac{1}{2} \cdot 0.0 2^{2} = \frac{0.0004}{2}

= ln (205) - ln (200) + 0.25 (\frac{0.0004}{2} - 0.05)

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lo g_{a} (2 x) + 2 (lo g_{a} (x) - lo g_{a} (y))

1 + 2 lo g_{10} (x) - lo g_{10} (y)

What is ln(205/200)+(1/2*0.02^2-0.05)*0.25 ?
The solution to ln(205/200)+(1/2*0.02^2-0.05)*0.25 is ln(205)-ln(200)+0.25((0.0004)/2-0.05)