Question

7log16/15+5log25/24+3log81/80

Answer 1

I assume you want to simplify in some manner.

7(4log2-(log3+log5)) + 5(2log5-(3log2+log3)) + 3(4log3-(4log2+log5))

now combine like logs, and you wind up with

log2

Or, you can combine the factors first:

7log16/15+5log25/24+3log81/80
log ((2^4/(3*5))^7 * (5^2/(2^3*3))^5 * (3^4/(2^4*5))^3)
= log(2^28 3^-7 5^-7 * 5^10 2^-15 3^-5 * 3^12 2^-12 5^-3)
= log(2^(28-15-12) 3^(-7-5+12) 5^(-7+10-3))
= log(2^1 3^0 5^0)
= log2