What is join (15ln(59/38))/(ln(2)) ?

The solution to join (15ln(59/38))/(ln(2)) is (ln(\frac{59^{15})/(38^{15)})}{ln(2)}

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join (15ln(59/38))/(ln(2))

join

\frac{15 ln ( \frac{59}{38} )}{ln ( 2 )}

\frac{ln ( \frac{5 9 ^{15}}{3 8 ^{15}} )}{ln ( 2 )}

Decimal

9.52073 \dots

Solution steps

\frac{15 ln ( \frac{59}{38} )}{ln ( 2 )}

Apply log rule:

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

15 ln (\frac{59}{38}) = ln ((\frac{59}{38})^{15})

= \frac{ln ( ( \frac{59}{38} ) ^{15} )}{ln ( 2 )}

(\frac{59}{38})^{15} = \frac{5 9 ^{15}}{3 8 ^{15}}

= \frac{ln ( \frac{5 9 ^{15}}{3 8 ^{15}} )}{ln ( 2 )}

\frac{81}{4} ln (3)

\frac{1}{5} ln (\frac{2}{3})

- \frac{1}{2} lo g_{10} (2)

- lo g_{10} (2.5 \cdot 1 0^{- 8})

3 ln (\frac{14}{13})

What is join (15ln(59/38))/(ln(2)) ?
The solution to join (15ln(59/38))/(ln(2)) is (ln(\frac{59^{15})/(38^{15)})}{ln(2)}