Question

(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)/<b>(</b>(log₃(√10+1)+log₃(√10-1)log₇ 2 <b>)</b>

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

Answer 3

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