1. ## Logarithmic function question

Hi guys I am back,

So I'm doing logarithmic function exercises in textbook and need to evaluate some. This one is:

log(base)8 .25

I understand this but would like to understand the easiest procedure to go from .25 to its equivalent 8^-2/3

Thanks

Edit: my usual way is to write out the exp form like: 8^x = 1/4, but then I get stuck ha

2. Originally Posted by DannyMath

Edit: my usual way is to write out the exp form like: 8^x = 1/4, but then I get stuck ha
then get "unstuck" ...

$\displaystyle 8^x = \frac{1}{4}$

$\displaystyle (2^3)^x = \frac{1}{2^2}$

$\displaystyle 2^{3x} = 2^{-2}$

$\displaystyle 3x = -2$

$\displaystyle x = -\frac{2}{3}$

3. See that's what I needed, I keep learning these little things along the way and understanding more and more. It's not like I'm asking for answers I hope. HAHA

Thank you!

4. It comes down to asking yourself

8 and 4 are powers of what number?

5. Yes that is much clearer to me now. Thank you!