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Logarithm Question!!!



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zordoloom
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What's the question?

aceace
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\[\log_{4}0.125 \] ... evaluate without a calculator

zordoloom
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Oh, that's simple. Do you know how to do base change?

aceace
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no base change allowed

zordoloom
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You divide (log(0.125)/(log(4))

zordoloom
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There is really no other way to enter it in a calculator

zepdrix
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So the log equals some unknown quantity, let's call it x.
\[\large \log_{4} 0.125=x\]
Do you know how to rewrite this as an exponential?

zordoloom
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Oh, sorry, I didn't notice the no calculator allowed. Okay....

aceace
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i got it though.... i'll show you the method and tell me if its right

aceace
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\[\log_{4} 8\] then \[(\log_{4}2 + \log_{4}4)\] then (0.5 +1) then 1.5

zepdrix
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Hmm yah I suppose that works! :) That's a little different than how I would have done it. But it get's you familiar with log rules, so that's good :D

geerky42
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0.125 = 1/8 and let \(x = \log_4\dfrac{1}{8}\)
Convert it to exponent form, then find x

zepdrix
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Yah that was the other way c: hehe
Either way though!

geerky42
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Yeah, just saying.