What is e^{3/2 (ln(90000)-5/3 ln(10000))} ?

The solution to e^{3/2 (ln(90000)-5/3 ln(10000))} is e^{(3ln((9\sqrt[3]{10})/(1000)))/2}

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simplify e^{3/2 (ln(90000)-5/3 ln(10000))}

simplify

e^{\frac{3}{2} (l n (90000) - \frac{5}{3} l n (10000))}

Decimal Notation

0.0027

Solution steps

e^{\frac{3}{2} (l n (90000) - \frac{5}{3} l n (10000))}

Apply log rule:

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

\frac{5}{3} ln (10000) = ln (1000 0^{\frac{5}{3}})

= e^{\frac{3}{2} (l n (90000) - l n (1000 0^{\frac{5}{3}}))}

Apply log rule:

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

ln (90000) - ln (1000 0^{\frac{5}{3}}) = ln (\frac{90000}{1000 0 ^{\frac{5}{3}}})

= e^{\frac{3}{2} l n (\frac{90000}{1000 0 ^{\frac{5}{3}}})}

Multiply

= e^{\frac{3 l n ( \frac{9}{100 \cdot 1 0 ^{\frac{2}{3}}} )}{2}}

- lo g_{10} ((1.8 \cdot 1 0^{- 5}) (0.1))

ln (\frac{439.7918}{1105.7918})

ln (\frac{0.9636}{1 - 0.9636})

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

1 - 4 ln (\frac{5}{4})

What is e^{3/2 (ln(90000)-5/3 ln(10000))} ?
The solution to e^{3/2 (ln(90000)-5/3 ln(10000))} is e^{(3ln((9\sqrt[3]{10})/(1000)))/2}