logbase8 1/32=x

Question

logbase8 1/32=x

anonymous · Answer

$$\log_{8}1/32 $$

anonymous · Answer

i dont know if i dont understand but its a base of 8 not 2

myininaya · Answer

$$\log_8(2^{-5})=x$$
$$2^{-5}=8^x$$
$$2^{-5}=2^{3 x}  \text{ since } 2^3=8$$
$$=>-5=3x$$

myininaya · Answer

Any questions?

myininaya · Answer

I left the last step for you.

anonymous · Answer

sorry but im still confuse

accessdenied · Answer

would it make more sense to you to think of the logarithm as a "what exponent of (base) will get me (given number)", the 'definition' of the logarithm?  I.e

You have a base of 8, and they give you 1/32, which is equal to 2^-5.
What exponent on the base, 8, will get you to 2^-5?  Well, maybe it'd make sense if we had the same bases.  The cube root (which is rational exponent of 1/3) gets our bases equal.

8^(1/3) = 2, so 2^3 = 8
What exponent on 2^3 will get us to 2^-5?  Well, we'll need the exponent to cancel out the 3 and give us -5.  That'd be a fraction, -5/3 -- 3/3 = 1, and -5 is remaining, which leaves 2^-5.

myininaya · Answer

Can you tell me which step troubles you?

anonymous · Answer

the very last part were -5=3x i dont get how to apply that to the problem dont see how that connects

anonymous · Answer

thanks luis by seeing the steps out it makes sense what the others are talking about

myininaya · Answer

lol I'm glad you understand my steps now.

anonymous · Answer

|dw:1330893856882:dw| do the 2's have to be the same on both sides or can one be a 2 and the othe be a 4 if that makes sence