problem with understanding logarithm

Question

Could anyone explain why this is true?$$\log_{a}{b^{\log_{a}c}} = \log_{a}{c}\log_{a}{b}$$

I think it's related to $a^{\log_{a}{b}}=b$ but I can't link it ...

score 5 · Accepted Answer · answered Nov 30 '13 at 09:59

5

Hint: $$M\log_{a}{x}=\log_{a}{(x^M)}$$

answered Nov 30 '13 at 09:59

math110

1

so just $\log_{a}{c}\log_{a}{b} = \log_{a}{b^{\log_{a}{c}}}$ , assuming $M=\log_{a}{c}$ ? – Mark Nov 30 '13 at 10:02
Yes,That's my mean – math110 Nov 30 '13 at 10:26

1 Answers1