What is 9ln(7)-9ln(5) ?

The solution to 9ln(7)-9ln(5) is ln(40353607/1953125)

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simplify 9ln(7)-9ln(5)

simplify

9 ln (7) - 9 ln (5)

ln (\frac{40353607}{1953125})

Decimal Notation

3.02825 \dots

Solution steps

9 ln (7) - 9 ln (5)

Apply log rule:

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

9 ln (7) = ln (7^{9})

= ln (7^{9}) - 9 ln (5)

Apply log rule:

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

9 ln (5) = ln (5^{9})

= ln (7^{9}) - ln (5^{9})

Apply log rule:

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

ln (7^{9}) - ln (5^{9}) = ln (\frac{7 ^{9}}{5 ^{9}})

= ln (\frac{7 ^{9}}{5 ^{9}})

\frac{7 ^{9}}{5 ^{9}} = \frac{40353607}{1953125}

= ln (\frac{40353607}{1953125})

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

- 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})