What is 9ln(18)-5ln(10) ?

The solution to 9ln(18)-5ln(10) is ln(6198727824/3125)

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simplify 9ln(18)-5ln(10)

simplify

9 ln (18) - 5 ln (10)

ln (\frac{6198727824}{3125})

Solution steps

9 ln (18) - 5 ln (10)

Apply log rule:

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

9 ln (18) = ln (1 8^{9})

= ln (1 8^{9}) - 5 ln (10)

Apply log rule:

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

5 ln (10) = ln (1 0^{5})

= ln (1 8^{9}) - ln (1 0^{5})

Apply log rule:

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

ln (1 8^{9}) - ln (1 0^{5}) = ln (\frac{1 8 ^{9}}{1 0 ^{5}})

= ln (\frac{1 8 ^{9}}{1 0 ^{5}})

\frac{1 8 ^{9}}{1 0 ^{5}} = \frac{6198727824}{3125}

= ln (\frac{6198727824}{3125})

- ln (e^{x} + 1) + ln (2)

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

lo g_{10} (z^{6})

lo g_{2} (3 t) + lo g_{2} (5 t)

- lo g_{10} (5.5 \cdot 1 0^{- 11})

What is 9ln(18)-5ln(10) ?
The solution to 9ln(18)-5ln(10) is ln(6198727824/3125)