anonymous
  • anonymous
Given that log(a)b = 3.14 and log(a)c = 2.45, find: log(a)√(bc) explanation + answer if you can please!
Mathematics
schrodinger
  • schrodinger
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nowhereman
  • nowhereman
By log(a)b do you mean logarithm of b for base a?
anonymous
  • anonymous
yea, so: \[\log_{a} b =3.14\] etc...
anonymous
  • 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 \[\log_ab^n \equiv n \log_ab \text{ with}\ n = \frac{1}{2}\]

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

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