Question

Help! Simplify this expression! Thanks!!

Answer 1

use this here ,

log{2 base (e -1) } + log { (e -1) base 2 }

log { 2 base (e -1) } + 1/ log{2 base (e -1) }

we know,
e = 2.7 ( approx )
so, e -1 = 1.7 >1 and 2>1
so, log {2 base (e -1) } will be positive .

so,
1/log{ 2 base (e -1) } is also positive.

now, use AM≥ GM

[ log{ 2 base (e -1) } +1/log{ 2 base (e -1) } ] ≥ 2

hence,
log{2 base (e -1) } + log { (e -1) base 2 } ≥ 2

so, here , 2 is smaller ,



now,

Answer 2

hope this helps........