What is 1/2 ln(130/100) ?

The solution to 1/2 ln(130/100) is 1/2 ln(130)-ln(10)

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simplify 1/2 ln(130/100)

simplify

\frac{1}{2} ln (\frac{130}{100})

\frac{1}{2} ln (130) - ln (10)

Decimal Notation

0.13118 \dots

Solution steps

\frac{1}{2} ln (\frac{130}{100})

Apply log rule:

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

ln (\frac{130}{100}) = ln (130) - ln (100)

= \frac{1}{2} (ln (130) - ln (100))

ln (100) = 2 ln (10)

= \frac{1}{2} (ln (130) - 2 ln (10))

Apply the distributive law:

a (b - c) = ab - a c

a = \frac{1}{2}, b = ln (130), c = 2 ln (10)

= \frac{1}{2} ln (130) - \frac{1}{2} \cdot 2 ln (10)

= \frac{1}{2} ln (130) - 2 \cdot \frac{1}{2} ln (10)

2 \cdot \frac{1}{2} ln (10) = ln (10)

= \frac{1}{2} ln (130) - ln (10)

- lo g_{10} (1 \cdot 1 0^{- 1.75})

6.1 + lo g_{10} (\frac{24.5}{1.01})

ln (- e^{- x} (1 + \frac{1}{3} e^{- 2 x}))

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

ln (7) + ln (8)