What is 38*ln(400/600)-8.314*ln(1/10) ?

The solution to 38*ln(400/600)-8.314*ln(1/10) is ln(41.93070…)

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simplify 38ln(400/600)-8.314ln(1/10)

simplify

38 \cdot ln (\frac{400}{600}) - 8.314 \cdot ln (\frac{1}{10})

ln (41.93070 \dots)

Decimal Notation

3.73601 \dots

Solution steps

38 ln (\frac{400}{600}) - 8.314 ln (\frac{1}{10})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

38 ln (\frac{400}{600}) = ln ((\frac{400}{600})^{38})

= ln ((\frac{400}{600})^{38}) - 8.314 ln (\frac{1}{10})

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8.314 ln (\frac{1}{10}) = ln ((\frac{1}{10})^{8.314})

= ln ((\frac{400}{600})^{38}) - ln ((\frac{1}{10})^{8.314})

Apply log rule:

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

ln ((\frac{400}{600})^{38}) - ln ((\frac{1}{10})^{8.314}) = ln (\frac{( \frac{400}{600} ) ^{38}}{( \frac{1}{10} ) ^{8.314}})

= ln (\frac{( \frac{400}{600} ) ^{38}}{( \frac{1}{10} ) ^{8.314}})

\frac{( \frac{400}{600} ) ^{38}}{( \frac{1}{10} ) ^{8.314}} = 41.93070 \dots

= ln (41.93070 \dots)

ln (\frac{1}{5}) - e^{(- 5^{3})}

8 \cdot ln (\frac{8}{9.1161})

lo g_{10} (\frac{1}{2.5 \cdot 1 0 ^{- 9}})

- 2 ln (\frac{3 e ^{- n^{3} + n x}}{x})

\frac{1}{3} ln ((x + 2)^{3}) + \frac{1}{2} ln (\frac{x}{( x ^{2} + 3 x + 2 ) ^{2}})

What is 38*ln(400/600)-8.314*ln(1/10) ?
The solution to 38*ln(400/600)-8.314*ln(1/10) is ln(41.93070…)