How to prove this Logarithmic identity?

Question

I am just learning logs, and can't get this one out ? How to prove that

$$ \log_a (b) \cdot \log_b (c) = \log_a (c) $$ in the format : log [base]([argument]) thank you .

Try to translate into a statement about exponentials, by introducing new variables: $\log_a b= x$, so $a^x=b$, etc. — Michael Weiss, Mar 15 '14 at 03:17

score 2 · Answer 1 · answered Mar 05 '14 at 13:39

2

Express all in base $\;a\;$ (change of base property):

$$\log_ab\cdot\log_bc=\log_ab\frac{\log_ac}{\log_ab}=\ldots$$

answered Mar 05 '14 at 13:39

DonAntonio

I feel embarrased ... I really don't believe that i did not see this . Thank you .ps don't have enough credit to vote up. – FutureSci Mar 05 '14 at 13:44

1 Answers1