What is 8.314(59+273)ln(0.286)-ln(1.99*10^{11}) ?

The solution to 8.314(59+273)ln(0.286)-ln(1.99*10^{11}) is 2760.248ln(0.286)-ln(1.99)-11ln(10)

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simplify 8.314(59+273)ln(0.286)-ln(1.99*10^{11})

simplify

8.314 (59 + 273) ln (0.286) - ln (1.99 \cdot 1 0^{11})

2760.248 ln (0.286) - ln (1.99) - 11 ln (10)

Decimal Notation

- 3481.19418 \dots

Solution steps

8.314 (59 + 273) ln (0.286) - ln (1.99 \cdot 1 0^{11})

Apply log rule:

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

ln (1.99 \cdot 1 0^{11}) = ln (1.99) + ln (1 0^{11})

= 8.314 ln (0.286) (59 + 273) - (ln (1.99) + ln (1 0^{11}))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (1 0^{11}) = 11 ln (10)

= 8.314 (59 + 273) ln (0.286) - (ln (1.99) + 11 ln (10))

8.314 (59 + 273) ln (0.286) = 2760.248 ln (0.286)

= 2760.248 ln (0.286) - (11 ln (10) + ln (1.99))

- (ln (1.99) + 11 ln (10)) : - ln (1.99) - 11 ln (10)

= 2760.248 ln (0.286) - ln (1.99) - 11 ln (10)

- lo g_{10} (7.2 \cdot 1 0^{- 5})

2 ln (- 1) - 2 ln (- 2)

ln \frac{( \frac{( - \frac{4}{3} )}{( - \frac{7}{6} )} )}{2}

2 ln (2) + 3 ln (3)

ln (\frac{0.063}{0.0295})

What is 8.314(59+273)ln(0.286)-ln(1.99*10^{11}) ?
The solution to 8.314(59+273)ln(0.286)-ln(1.99*10^{11}) is 2760.248ln(0.286)-ln(1.99)-11ln(10)