Logarithm Question!!!

Question

anonymous · Answer

What's the question?

anonymous · Answer

$$\log_{4}0.125 $$ ... evaluate without a calculator

anonymous · Answer

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

anonymous · Answer

no base change allowed

anonymous · Answer

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

anonymous · Answer

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

zepdrix · Answer

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?

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

$$-\log_{4} 8$$ then $$-(\log_{4}2 +  \log_{4}4)$$ then -(0.5 +1) then -1.5

zepdrix · Answer

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 · Answer

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

zepdrix · Answer

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

geerky42 · Answer

Yeah, just saying.