What is join (ln(9/1024))/(2ln(243/16)) ?

The solution to join (ln(9/1024))/(2ln(243/16)) is (ln(9/1024))/(ln(59049/256))

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join (ln(9/1024))/(2ln(243/16))

join

\frac{ln ( \frac{9}{1024} )}{2 ln ( \frac{243}{16} )}

\frac{ln ( \frac{9}{1024} )}{ln ( \frac{59049}{256} )}

Decimal Notation

- 0.87011 \dots

Solution steps

\frac{ln ( \frac{9}{1024} )}{2 ln ( \frac{243}{16} )}

Apply log rule:

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

2 ln (\frac{243}{16}) = ln ((\frac{243}{16})^{2})

= \frac{ln ( \frac{9}{1024} )}{ln ( ( \frac{243}{16} ) ^{2} )}

(\frac{243}{16})^{2} = \frac{24 3 ^{2}}{1 6 ^{2}}

= \frac{ln ( \frac{9}{1024} )}{ln ( \frac{24 3 ^{2}}{1 6 ^{2}} )}

\frac{24 3 ^{2}}{1 6 ^{2}} = \frac{59049}{256}

= \frac{ln ( \frac{9}{1024} )}{ln ( \frac{59049}{256} )}

lo g_{10} (\frac{y z ^{3}}{x ^{5}})

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

lo g_{8} (\frac{4 5}{6})

6 ln (x) + 4 ln (y) - 3 ln (z)

lo g_{10} (\frac{a ^{2} ab}{( ab ) ^{2}})

What is join (ln(9/1024))/(2ln(243/16)) ?
The solution to join (ln(9/1024))/(2ln(243/16)) is (ln(9/1024))/(ln(59049/256))