What is simplify-ln((0.8-3/5)/(1-3/5)) ?

The solution to simplify-ln((0.8-3/5)/(1-3/5)) is -ln(0.8-3/5)+ln(2/5)

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simplify-ln((0.8-3/5)/(1-3/5))

simplify

- ln (\frac{0.8 - \frac{3}{5}}{1 - \frac{3}{5}})

- ln (0.8 - \frac{3}{5}) + ln (\frac{2}{5})

Decimal Notation

0.69314 \dots

Solution steps

- ln (\frac{0.8 - \frac{3}{5}}{1 - \frac{3}{5}})

Apply log rule:

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

ln (\frac{0.8 - \frac{3}{5}}{1 - \frac{3}{5}}) = ln (0.8 - \frac{3}{5}) - ln (1 - \frac{3}{5})

= - (ln (- \frac{3}{5} + 0.8) - ln (- \frac{3}{5} + 1))

Join

1 - \frac{3}{5} : \frac{2}{5}

= - (ln (- \frac{3}{5} + 0.8) - ln (\frac{2}{5}))

Distribute parentheses

= - (ln (0.8 - \frac{3}{5})) - (- ln (\frac{2}{5}))

Apply minus-plus rules

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

= - ln (0.8 - \frac{3}{5}) + ln (\frac{2}{5})

ln (\frac{30000}{25000})

\frac{3 ln ( 5 ) - 3 ln ( 7 )}{2 ln ( 7 ) - ln ( 5 )}

ln (\frac{2 i + 1}{- 1})

\frac{5 ln ( 3 )}{ln ( \frac{2}{3} )}

(2 \cdot 8.314) \cdot ln (\frac{1.5}{7})

What is simplify-ln((0.8-3/5)/(1-3/5)) ?
The solution to simplify-ln((0.8-3/5)/(1-3/5)) is -ln(0.8-3/5)+ln(2/5)