Suppose that log𝑥𝑦^3 = 1 and log𝑥^2𝑦=1. What is the value of log𝑥𝑦?
log𝑥𝑦^3 = 1
logx + 3logy = 1 ---> logx = 1 - 3logy
log𝑥^2𝑦=1
2logx + logy = 1
use substitution:
2(1 - 3logy) + logy = 1
2 - 6logy + logy = 1
5logy = 1
logy = 1/5
then logx = 1 - 3logy
= 1 - 3/5 = 2/5
log (xy) = logx + log y = 2/5 + 1/5 = 3/5