ln(ln³²(e³²))
= 32 ln(ln(e³²))
= 32 ln(32 ln(e))
= 32 ln 32
= 32 ln 2^5
= 160 ln 2.
Not sure of your notation, on the first 32. Is that 32 a constant or exponent? But here is what my interpretation is:
ln(e^x) = x
So, ln(1) = 0
ln [ { ln(e^32) }^32 ]
= 32*ln[ {ln(e^32)} ]
= 32*ln[ {32*ln(e)} ]
= 32*ln[ {32*1} ]
= 32*ln(32)
= 32*ln(2^5)
= 32*5*ln(2)
= 160*ln(2)
My calculator says
110.9035488 89591249506 75713943331
but the decimals don't follow any particular pattern. Hmmm.
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Verified answer
ln(ln³²(e³²))
= 32 ln(ln(e³²))
= 32 ln(32 ln(e))
= 32 ln 32
= 32 ln 2^5
= 160 ln 2.
Not sure of your notation, on the first 32. Is that 32 a constant or exponent? But here is what my interpretation is:
ln(e^x) = x
So, ln(1) = 0
ln [ { ln(e^32) }^32 ]
= 32*ln[ {ln(e^32)} ]
= 32*ln[ {32*ln(e)} ]
= 32*ln[ {32*1} ]
= 32*ln(32)
= 32*ln(2^5)
= 32*5*ln(2)
= 160*ln(2)
My calculator says
110.9035488 89591249506 75713943331
but the decimals don't follow any particular pattern. Hmmm.