What is simplify-ln((3.8)/(16))-ln(5/16) ?

The solution to simplify-ln((3.8)/(16))-ln(5/16) is -ln(0.07421875)

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simplify-ln((3.8)/(16))-ln(5/16)

simplify

- ln (\frac{3.8}{16}) - ln (\frac{5}{16})

- ln (0.07421875)

Decimal Notation

2.60073 \dots

Solution steps

- ln (\frac{3.8}{16}) - ln (\frac{5}{16})

Rewrite

- ln (\frac{3.8}{16}) - ln (\frac{5}{16})

- (ln (\frac{3.8}{16}) + ln (\frac{5}{16}))

= - (ln (\frac{5}{16}) + ln (\frac{3.8}{16}))

Apply log rule:

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

ln (\frac{3.8}{16}) + ln (\frac{5}{16}) = ln (\frac{5}{16} \cdot \frac{3.8}{16})

= - ln (\frac{5}{16} \cdot \frac{3.8}{16})

\frac{3.8}{16} \cdot \frac{5}{16} = 0.07421875

= - ln (0.07421875)

- lo g_{10} (4.51 \cdot 1 0^{- 6})

- lo g_{10} (2.3 \cdot 1 0^{- 4})

ln (\frac{75.5}{49.2})

ln (\frac{1}{2} e^{- k t})

5 ln (\frac{3}{4}) + \frac{5}{2} + \frac{3 ( - ln ( 3 ) - 3 ln ( \frac{3}{4} ) )}{2}

What is simplify-ln((3.8)/(16))-ln(5/16) ?
The solution to simplify-ln((3.8)/(16))-ln(5/16) is -ln(0.07421875)