What is n*(35.2*ln(420/293)-8.314*ln(2500/500)) ?

The solution to n*(35.2*ln(420/293)-8.314*ln(2500/500)) is nln(0.49362…)

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simplify n(35.2ln(420/293)-8.314*ln(2500/500))

simplify

n \cdot (35.2 \cdot ln (\frac{420}{293}) - 8.314 \cdot ln (\frac{2500}{500}))

n ln (0.49362 \dots)

Solution steps

n (35.2 ln (\frac{420}{293}) - 8.314 ln (\frac{2500}{500}))

Apply log rule:

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

35.2 ln (\frac{420}{293}) = ln ((\frac{420}{293})^{35.2})

= (ln ((\frac{420}{293})^{35.2}) - 8.314 ln (\frac{2500}{500})) n

Apply log rule:

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

8.314 ln (\frac{2500}{500}) = ln ((\frac{2500}{500})^{8.314})

= (ln ((\frac{420}{293})^{35.2}) - ln ((\frac{2500}{500})^{8.314})) n

Apply log rule:

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

ln ((\frac{420}{293})^{35.2}) - ln ((\frac{2500}{500})^{8.314}) = ln (\frac{( \frac{420}{293} ) ^{35.2}}{( \frac{2500}{500} ) ^{8.314}})

= ln (\frac{( \frac{420}{293} ) ^{35.2}}{( \frac{2500}{500} ) ^{8.314}}) n

\frac{( \frac{420}{293} ) ^{35.2}}{( \frac{2500}{500} ) ^{8.314}} = 0.49362 \dots

= n ln (0.49362 \dots)

lo g_{7} (\frac{3 x ^{4}}{y})

\frac{1}{7} ln ((x + 2)^{7}) + \frac{1}{2} ln (x) - ln (x^{2} + 3 x + 2) 2

- ln (4) + ln (3) + ln (3) - ln (2)

3 lo g_{3^{^{'}}} (- 2 lo g_{6^{^{'}}} (x))

- ln (\frac{t}{1 - t})

What is n*(35.2*ln(420/293)-8.314*ln(2500/500)) ?
The solution to n*(35.2*ln(420/293)-8.314*ln(2500/500)) is nln(0.49362…)