What is simplify-ln(4/5) ?

The solution to simplify-ln(4/5) is -2ln(2)+ln(5)

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simplify-ln(4/5)

simplify

- ln (\frac{4}{5})

- 2 ln (2) + ln (5)

Decimal Notation

0.22314 \dots

Solution steps

- ln (\frac{4}{5})

Apply log rule:

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

ln (\frac{4}{5}) = ln (4) - ln (5)

= - (ln (4) - ln (5))

ln (4) = 2 ln (2)

= - (2 ln (2) - ln (5))

Distribute parentheses

= - (2 ln (2)) - (- ln (5))

Apply minus-plus rules

- (- a) = a, - (a) = - a

= - 2 ln (2) + ln (5)

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ln (\frac{( 2 y + 1 ) ^{5}}{y ^{2} + 1})

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ln (\frac{( 1 + 5 )}{2})