What is (-10*ln(80/180))/(ln(55/180)+ln(80/180)) ?

The solution to (-10*ln(80/180))/(ln(55/180)+ln(80/180)) is -(10ln(4/9))/(ln(11/81))

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simplify (-10*ln(80/180))/(ln(55/180)+ln(80/180))

simplify

\frac{- 10 \cdot ln ( \frac{80}{180} )}{ln ( \frac{55}{180} ) + ln ( \frac{80}{180} )}

- \frac{10 ln ( \frac{4}{9} )}{ln ( \frac{11}{81} )}

Decimal Notation

- 4.06164 \dots

Solution steps

\frac{- 10 ln ( \frac{80}{180} )}{ln ( \frac{55}{180} ) + ln ( \frac{80}{180} )}

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{55}{180}) + ln (\frac{80}{180}) = ln (\frac{55}{180} \cdot \frac{80}{180})

= \frac{- 10 ln ( \frac{80}{180} )}{ln ( \frac{55}{180} \cdot \frac{80}{180} )}

\frac{55}{180} \cdot \frac{80}{180} = \frac{11}{81}

= \frac{- 10 ln ( \frac{80}{180} )}{ln ( \frac{11}{81} )}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{10 ln ( \frac{80}{180} )}{ln ( \frac{11}{81} )}

\frac{80}{180} = \frac{4}{9}

= - \frac{10 ln ( \frac{4}{9} )}{ln ( \frac{11}{81} )}

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What is (-10*ln(80/180))/(ln(55/180)+ln(80/180)) ?
The solution to (-10*ln(80/180))/(ln(55/180)+ln(80/180)) is -(10ln(4/9))/(ln(11/81))