Without using a calculator, which of these is larger: log8 62 or log7 50. Why

Because log8 64 = 2 then log8 62 must be <2
similarly log7 49 = 2 so log7 50 must be >2
log7 50 is larger

log7 50

The reason i can tell is because 7^2<50

And 8^2>62

So therefore log7 is the bigger one.

My thing is by no means a shortcut or anything i just am able to recognize that logs involve squaring numbers and bases

log8 62 is under 2, log7 50 is over 2

8^2 = 64 and 7^2 = 49

log8 62 < log8 64 = 2
log7 50 > log7 49 = 2
So, log7 50 > log8 62

log7 50 is larger