(2*log7 16)/(log3(√10+1)+log3(√10-1)log7 2

Answer 1

I suspect a typo, since

log3(√10+1)+log3(√10+1) = log3(10-1) = log3(9) = 2

the log7 of powers of 2 is not amenable to simplification.

Is there a typo? At the very least, the parentheses are not balanced.

Answer 2

Fractions have implicit parenthese around the denominator and numerator.

I have a feeling that the two log₃ terms both belong to the denominator, in which case the expression should have been written, according to the BEDMAS rules,

(2*log₇ 16)/((log₃(√10+1)+log₃(√10-1)log₇ 2 )

in which case:
(2*log₇2⁴)/((log₃(√10+1)(√10-1) log₇ 2 )
=(8*log₇2)/((log₃(10-1) log₇ 2 )
=(8*log₇2)/((log₃(9) log₇ 2 )
=(8*log₇2)/(2 log₇ 2 )
=4

Answer 3

Just a lucky guess, but you were right in the first place!