Question

Given that log(a)b = 3.14 and log(a)c = 2.45, find:
log(a)√(bc)

explanation + answer if you can please!

Answer 1

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

Answer 2

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

Answer 3

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 \[\log_ab^n \equiv n \log_ab \text{ with}\ n = \frac{1}{2}\]

Answer 4

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