# How to prove this Logarithmic identity?

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 .

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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 3:17

Express all in base $\;a\;$ (change of base property):
$$\log_ab\cdot\log_bc=\log_ab\frac{\log_ac}{\log_ab}=\ldots$$