Express log x in terms of log a, log b, and log c: x= radical(ab)/ c^2?

Take the log of both sides.





logx = log [ sqrt(ab)/ c^2]





Now change the form of the expression on the right.


logx = log[sqrt(ab)] - log(c^2)


logx = log[(ab)^0.5] - log(c^2)


logx = 1/2 log(ab) - 2log(c)


logx = 1/2 log(a) + 1/2 log(b) - 2log(c)

Express log x in terms of log a, log b, and log c: x= radical(ab)/ c^2?
x= √(ab)/ c²


x= (ab)^(1/2)/ c²





log(x) = log((ab)^(1/2)/ c²)


log(x) = log((ab)^(1/2)) - log(c²)


log(x) = 1/2 log(ab) - 2log(c)


log(x) = 1/2 log(a) + 1/2 log(b) - 2 log(c)