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Logarithm Question!!!



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aceace
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Evaluate in terms of p \[\log_{c} b\] if ... \[\log_{b}a =p \] and c=a^2

hartnn
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put a = \(\sqrt c\) in that
and tell me what u get ?

aceace
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log _b (root c) = p

hartnn
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right , now use the property that \(\log x^y=y \log x\)
so what will be
\(\log_b c^{1/2} = ? \)

aceace
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1/2 (log_b (c))

hartnn
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right, that is p, so what is (log_b (c)) = ?

dumbcow
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what a fun problem...i won't spoil the solution and let hartnn explain the steps

aceace
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um....2p

hartnn
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thats correct.
then use the property that
\(\huge \log_xy=\frac{\log y}{\log x} = \frac{1}{\log_yx}\)

hartnn
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(log_b (c)) = 2p
so whats (log_c (b)) = ?

aceace
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lol i am not fimiliar with that property.. but it equals 1/(2p)

hartnn
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yes, 1/(2p) is correct.
its one of the very useful properties of log.
u want a list of all the log properties ?

aceace
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yes please XD


aceace
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thank you!

hartnn
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welcome ^_^