How do you solve this equation? Does it contain log?

log a=0.16 and log b=-2.4. Find log ((sqrt(b))/(1000a)). After I expand it I'm not sure if it's a full number or if it contains log

Anonymous2010-04-02T16:30:19Z

Favorite Answer

Note that:

log[√b/(1000a)]
= log(√b) - log(1000a) <== Use log(a/b) = log(a) - log(b)
= log(√b) - [log(1000) + log(a)] <== Use log(ab) = log(a) + log(b)
= log(√b) - [3 + log(a)]
= log(√b) - log(a) - 3
= (1/2)log(b) - log(a) - 3 <== Use log(a^b) = b*log(a).

Then, using the given information, we see that:

log[√b/(1000a)] = (1/2)log(b) - log(a) - 3 = (1/2)(-2.4) - 0.16 - 3 = -4.36.

I hope this helps!