Question

Without using your calculator, decide which of these is larger: log8 62 or log7 50. How confident are you of your answer? Explain your thinking

Answer 1

log8 62 = x1
8^x1= 62
8^2=64 >62 so x1<2.....1
log7 50=x2
7^x2=50
7^2=49<50 so x2>2......1

nw u got
x1<2
2<x2
x1<2<x2
x1<x2
log8 62<log7 50

Answer 2

In base 8, the log of 8 = 1 and log 8 of 64 = 2
so the base 8 log of 62 is slightly less than 2

In base 7, log 7 = 1 and base 7 log of 49 = 2
the base 7 log of 50 is slightly greater than 2.

So, the base 7 log of 49 is slightly larger than the base 8 log of 62.
and if you really need to calculate this- here is a good calculator:
http://1728.org/logrithm.htm