log base 2 into log base 2 into log base 3 into log base 5 into 125 whole cube
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log
2
(
log
2
(
log
5
(
125
)
)
)
=log2(log2(3))
=
log
2
(
log
2
(
3
)
)
=log2(ln(3)ln(2))
=
log
2
(
ln
(
3
)
ln
(
2
)
)
=log2(ln(3))−log2(ln(2))
=
log
2
(
ln
(
3
)
)
−
log
2
(
ln
(
2
)
)
=ln(ln(3))ln(2)−ln(ln(2))ln(2)
=
ln
(
ln
(
3
)
)
ln
(
2
)
−
ln
(
ln
(
2
)
)
ln
(
2
)
=ln(ln(3))−ln(ln(2))ln(2)
=
ln
(
ln
(
3
)
)
−
ln
(
ln
(
2
)
)
ln
(
2
)
≈0.664
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