What is ln(1/(95/100)) ?

The solution to ln(1/(95/100)) is -(ln(95)-2ln(10))

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simplify ln(1/(95/100))

simplify

ln (\frac{1}{\frac{95}{100}})

- (ln (95) - 2 ln (10))

Decimal Notation

0.05129 \dots

Solution steps

ln (\frac{1}{\frac{95}{100}})

Apply log rule:

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

ln (\frac{1}{\frac{95}{100}}) = ln (1) - ln (\frac{95}{100})

= ln (1) - ln (\frac{95}{100})

Apply log rule:

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

ln (\frac{95}{100}) = ln (95) - ln (100)

= ln (1) - (ln (95) - ln (100))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (95) - ln (100))

ln (100) = 2 ln (10)

= 0 - (ln (95) - 2 ln (10))

0 - (ln (95) - 2 ln (10)) = - (ln (95) - 2 ln (10))

= - (ln (95) - 2 ln (10))

ln (\frac{1}{w})

ln (\frac{\frac{1}{2} x}{x})

2 ln (2 t)

ln (\frac{9993000}{7000})

ln (\frac{4 x ^{2} - x - 2}{x ^{2} ( x + 1 )})