What is join-(1600ln(2/5))/(ln(2)) ?

The solution to join-(1600ln(2/5))/(ln(2)) is -(ln((2/5)^{1600}))/(ln(2))

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join-(1600ln(2/5))/(ln(2))

join

- \frac{1600 ln ( \frac{2}{5} )}{ln ( 2 )}

- \frac{ln ( ( \frac{2}{5} ) ^{1600} )}{ln ( 2 )}

Decimal Notation

2115.08495 \dots

Solution steps

- \frac{1600 ln ( \frac{2}{5} )}{ln ( 2 )}

Apply log rule:

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

1600 ln (\frac{2}{5}) = ln ((\frac{2}{5})^{1600})

= - \frac{ln ( ( \frac{2}{5} ) ^{1600} )}{ln ( 2 )}

0.4 \cdot lo g_{2} (\frac{1}{0.4}) + 0.6 \cdot lo g_{2} (\frac{1}{0.6})

\frac{3 ln ^{2} ( 5 )}{2} - 6 ln^{2} (2)

2 lo g_{8} (x) - \frac{1}{2} lo g_{8} (w) + 4 lo g_{8} (y)

ln (\frac{2.5}{1.5})

ln (\frac{( 31800000 )}{( 21800 )})

What is join-(1600ln(2/5))/(ln(2)) ?
The solution to join-(1600ln(2/5))/(ln(2)) is -(ln((2/5)^{1600}))/(ln(2))