## anonymous 5 years ago Given that log(a)b = 3.14 and log(a)c = 2.45, find: log(a)√(bc) explanation + answer if you can please!

1. nowhereman

By log(a)b do you mean logarithm of b for base a?

2. anonymous

yea, so: $\log_{a} b =3.14$ etc...

3. anonymous

If you use $\log_ab =c \iff \log_a \sqrt{b} = \frac{c}{2}$ and $\log_ab + \log_ac \equiv\log_a{bc}$ does that help? Note the first equation is a specific case of the rule $\log_ab^n \equiv n \log_ab \text{ with}\ n = \frac{1}{2}$

4. anonymous

ah i see, the radical sign was getting me confused with that initial rule. seeing it in practice makes things clear. cheers